It is easier to beg for forgiveness than ask for permission. I really hope you can keep those incredible speakers. Put some of her favourite music on and I'm sure she will change her mind.
Absolutely! As for more modern, I can't think of something that doesn't look like some type of weird sculpture or sounds worse. The JBL L300 is a timeless classic piece of furniture in its looks, especially if the grilles are done right and the glass tops are intact.
Please, please, try to get us some accurate and larger pictures taken with a smartphone or regular camera. If you can, size them to at least 800x600 or 1024x768. Show us the entirety of each speaker - front, top, sides, back, showing the condition of the walnut wood veneers, and the bottom if you can. Also, again show the woofer back label, legibly, and the front cone. Also, look again on the back of the cone for a printed 5 digit number in white starting with the number 5. That will tell us if its a genuine JBL cone, and which model cone it is. There are a number of recone kits that could fit the 136H frame, but the only one that is correct is the 2231 or 2235 recone kit with foam outer surround. The midrange and tweeter are not easily accessible but if the screws on the back access panel or on the front have no paint chipped away, they likely have never been messed with. The plastic slant lenses held on by velcro are important to leave in place when using and playing the speakers.
someone could have added or replaced the foam with a double roll cloth or paper surround but this will affect the woofer response and be different than is optimum for this system. However, the woofer can still be reconed to a correct system. The downside, is, if you're going to own classic JBL products, and appreciate them, their worth is highest, and their performance is closest to real JBL with real JBL parts, and they are not inexpensive to work on.
Don't get me wrong, I too think you've done well to get these at the price you paid, but they will need some additional work as you were anticipating. They will hold their value, or continue to appreciate, but only if they are done right and correctly.
The 136H woofer indicates you should have the JBL L300A Summit, which means you'll have an A behind the serial number, and you have the later 136H woofer with large round ferrite magnet instead of the earlier 136A alnico version. This woofer is exactly like the 2231H JBL Professional woofer, and both were superceded by the 2235H woofer. They all had the narrow roll foam surround.
As is, the woofer is probably more like the 2225H woofer, and will work reasonably well, but with less low bass extension, and more mid-bass. The woofer, as pictured from the ad, probably was reconed by the previous owner who may not have wanted to deal with the foam surround failing again.
I'd suggest turning the L-Pad controls a number of times as suggested to initially clean them up, then set at 0, for both, then back them down to -3 or -2. This helps cut the midrange and tweeter back a bit as the speaker are known to be a little forward or in your face. Set them up at least 6-10 feet apart and about 1 foot away from the back wall, and if possible, at least 2-3 feet away from side walls. Angle or toe in a little if needed. Sit in a chair that allows you to sit a little low, so that your head is even with the top of the speakers or a little lower, but if you haven't a chair like that, you may wish to tilt the speakers back a bit, or raise them up (carefully!) about 6 inches with some type of sturdy platform - a pair of Milwaukee brand furniture movers from Home Depot at $20 each is very useful for a stand and moving the speakers around and highly recommended.
Get some nice acoustic or vocal music (wife's favorites) and start there. Rock music is dynamite on L300's though too. Be sure you have good electronics to hook the speakers to, and don't be afraid to have the most powerful amp you can lay your hands on to use with them, they can take it. Just don't be too quick to up the volume, as these speakers are very dynamic and can surprise you with the power and volume they can create when the music calls for it.
If you've got a tiny living room, the L300's may be more than it can handle. If so, tell us the dimensions, and a set of JBL 4406/L20T's or slightly larger might be better suited. However, if at all possible, keep the L300's for when you have a bigger home. For many, these are once in a lifetime, bucket list speakers, and they just don't come around very often. If you like the way they sound, they can be a source of great fun and enjoyment, as well as an investment.
Don't give in to anything rash just yet, although I know the $$$ issue is very likely to pop up.
And like faber12, there are those of us who can help with the woofer issues when and if needed.