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Okay, I happen to really like to collect old JVC tt and Empire carts. You can search on here for the Empire cart inductance thread but it's most likely a Empire 66/x clone, if it measures out near 500 ohms dc resistance ( you can measure inductance if you have a meter for it, if not, dc resistance is the next best thing that can be used to see what your Empire 3000 II really is, it doesn't really matter what Empire labeled it because some are just mislabeled. You have to measure to be sure).
With that said, if it's a 66 clone, 239-PDE and what Empire called the$8-15 S912E (purple) and S913E (white) are going to be the best replacement stylus, if you can find them. I haven't seen orignal Empire stylus for sale in about 2 years unless it's a small batch found by someone's old stock pile. Voice of music sells a few modern Japanese made or Swiss made 4239 models. The 4 prefix is indication of aftermarket.
I have had good luck with the 4239-DEC from VOM. A tad bit brighter in upper mids-treble though. Works well for me and a bit of tone control (foreboded by some). If it has a bit higher resistance it's probably going to be a 2000/e clone and you will need the 4237 stylus for those. They are even harder to find an original stylus for sale.
As far as your JVC table and the weight of the counter balance. Your tt has that high compliance lightweight straight arm I believe? It's still going to be able to handle the blob style 2000/3000/4000 carts. I suspect you may have to use a scale and not go by what your counter weight shows. Get a cheap electronic scale of the web. About $8-15 can be found.
That's a really light headshell for your model and the cart is coming in around 6-7 grams. Should be fine. I use all my 66 models on a similar JVC table with similar arm. No problems.
Good luck with your quest and let us know how it goes for you!