Indeed the KLH model Six is an exceptional speaker and remains one of the best values available for about 80% of music listeners. It was voiced in a time when super deep bass wasn't prevalent, nor was the type of high frequency shimmer so common in electronically produced music of the last 20-30 years. It does voices, strings, small groups, orchestral music, and most rock from the 50s through the early 80s exceptionally well. And in truth, there's really nothing that I have found that gives it trouble other than extremely bass heavy electronica. Many argue that it's the ONLY speaker anyone should consider for less than $1000 unless they NEED deep bass. I won't go that far, but I can't fault people for suggesting it. It is only the lowest bass notes that are rolled off, and to my ears (which stop working around 18kHz), there is only a little roll-off on the top end. I would describe these as errors of omission rather than faults because it's better in my opinion, it is better to leave something out of the sound than to have it there but have it be wrong. Typically, if you find a pair that hasn't been refurbished, it's only a half day's work to restore the crossovers with parts of your choice, and re-dope the cloth surround (or re-foam, if you run into one with a foam surround).
Why you would NOT want to buy the Model Six: it's a large box speaker, and doesn't escape some "boxiness" in the sound. Unless you have a long relationship with open baffle, electrostatic, or other non-traditional speaker types, you won't even know what a boxy sound is, so probably don't worry about this too much.
It needs a shelf, stand or other way to orient the tweeter facing your ear level to sound its best. This can be challenging in some rooms, and some folks don't want to lay out extra dough for stands.
It doesn't put out max SPL the way some other speakers can. If you plan to use your system for parties, this isn't the speaker for you. Oh, it'll get LOUD, but it's not a "party speaker".
If you really want to hear the lowest organ notes, or you need to feel the bass in your chest and stomach from your various house/techno selections, this isn't going to do it. You could always add a sub, but that has its own drawbacks.
I haven't found the Model Six to pair "poorly" with anything, although there are some special pairings... Exceptional results can be had with lower powered receivers and amplifiers from the 60s through the mid 70s. I loved how the Six sounded with my Fisher X-100-B tube integrated amp, and was quite pleased with the sound when paired with the Marantz 1060. I was not especially impressed with it when paired with more modern, higher power solid state gear like a Classe CAP-80 or Musical Fidelity A300. This isn't to say it sounded bad, just that I think those power sources are better suited to other speaker offerings.
With more dough, there is more to work with. If you have the money to spend, I would look into Thiel CS series speakers. For around 800 you could likely get a set in good shape. These will deliver musical transparency that is among the best speakers out there. They disappear better than just about anything else I have ever heard. Many folks feel they need loads of power to sound good, but I have been mostly pleased with mine running on lower tube watts. I rarely "turn things up" though, and my space is about 40 sf smaller than yours. These speakers do really well with the Musical Fidelity A300, and Classe CAP-80, and I was very pleased with them hooked up to my Sony STR receiver.
I don't listen to a heck of a lot of newer speakers, but some that I like are the KEF LS50 (upper end of your range, and would need to be found 2nd hand to stay under a grand), B&W CDM-NT series, and the Elac Debut series speakers.
The KEF were speakers I wanted not to like. They are the darling of so many stereo magazines over the last 5 years that I felt like there was some ma$$aging of the reviewers? Or maybe the curved baffle, variety of colors, and unique driver arrangement tickled something in the typically white, male, luxury sedan driving, suburban living, upper management working, empty nester target audience that made them feel "hip" and "cool" and relevant again? Whatever the case, I found them to be similar to the Model Six not in sound character but in the fact that everything they do, they do really really well. Their sins are sins of omission rather than obviation. Coherent, smooth, articulate, relaxing without being boring at all... while not at the level of ribbons, opens, 'stats, and the like, they also have surprisingly little "boxiness" to the sound as long as you don't inadvertently box them in, room-wise. They are also not the last word in bass extension (what stand mount speaker is?), and placement can be trouble if you need to have them very near the rear wall (they are rear ported). Overall, though, if you have at least 75 watts of quality power, some room to work with in terms of placement, and enjoy the physical appearance, these are very hard to argue with.
The CDM-NT series are a little older... maybe 20 years old now? But they are still performers. They provide imaging that is truly TOP notch, a midrange that is tonally accurate, very pleasing, and in my experience they are especially good at reproducing the full, rich tone of instruments and voices. Clarinets or cellos don't just sound like clarinets and cellos... they sound like the specific clarinet or cello being played, and when you put on another recording with a different instrument/performer, you can tell it is a different instrument from the nuanced reproduction of the subtle tonal differences. Another thing that I like about the CDM-NT series is that they make the best of recordings that aren't as good as you might like. There are some speakers that are especially unforgiving of flaws in upstream components and in recordings. I found the CDM-CNT series speakers to lean the other way. They don't turn an aiwa minisystem into a $250k dream rig, but nor are they likely to leave you sitting there thinking "man, I really need to get a better _____" which can be a really nice thing. They are also fairly forgiving of lesser quality source material (for you used record shoppers). With that said, they will also rise to the occasion if and when you do get the upgrade bug. They have done well for me with lower wattage tube power, as well as solid state power. If your system leans strongly towards the "analytical" side of things, these may not be the right choice for you, though, and they do require a bit of playing around with setup to get the most out of them. You can get a pair of CDM-1NT bookshelf speakers for around $500 on the used market, and the CDM-7NT, which adds noticeable bass will only run you a bit more. If you are patient and lucky, you may find the top dog CDM-9-NT for under $1200.
The Elac Debut and Uni-Fi are also darlings of the audio review industry, but I didn't know that until well after I had heard a few different pairs and asked the owners "Hey, that sounds amazing! what are those speakers?" And especially the Debuts are also so cheap! I should also say that I haven't heard the floorstanders (which I think are in your price range, even new) but what I have heard of the bookshelf offerings has been impressive. So much so that I pretty much recommend them to any of my friends who want good sound, but don't care to get into deeper discussions about tonal character, vintage vs modern sound, etc. Just pair these with a good quality power source and enjoy. No more difficult than any other bookshelf speaker to set up, they offer a more complete sound than I expect from a package at that size (regardless of price). While some reviews say these are unforgiving of upstream component weaknesses, I'm of the opinion that the phraseology is wrong. I have never gotten the sense that they highlight, accentuate, or bring focus to upstream components. I would contend that a better description is "You won't get the best out of the Elacs with weaknesses upstream." They kind of take on the character of whatever you run them with, both in terms of power and source components. They're a great speaker if you want to learn what "The Marantz sound" is, or what "The Fisher sound" is. But they are also great speakers if you don't care about all that and just want good speakers to run with your above-average setup. *Not having heard the floorstanders, I can't be sure that all the positives of the bookshelf units will transfer, but Andrew Jones is no slouch, and I suspect that like the B&Ws above, the floorstanders in the Elac lineup will offer everything that is great about the bookshelf units, plus useful bass and more "fullness".
A few final thoughts:
I usually tell people "all things being equal, a floorstander will usually sound better", but of course that floorstander will probably be somewhat (or significantly) more expensive, so it's rare that all things really ARE equal. In your price range, there are a lot of quality floorstanders. A big mistake I made for a long time, and that many folks make with floorstanders, is plopping them down, tweaking a bit on the toe in and distance to walls, and calling it good. There are a lot of floorstanders that are around 38" to 45" tall, which, for me, puts the tweeter below my ear level when listening, and I have discovered that I was leaving a lot of SQ on the table by not properly adjusting them on the vertical axis, as well. This isn't something that I (or, probably most folks) think as much about with bookshelf speakers, because you know going in that you will need to get stands.
Hopefully there is something in here that is helpful! Best of luck on your hunt!