OP,
Welcome to the forum.
From what I can tell of your system you have a great opportunity for improvement. You have very good speakers capable of much better sound than you are likely getting.
It is really helpful to us to be able to see your whole system. There is a place under your user ID to put some photos and ID your equipment. You can see ours there as well. It is really helpful.
Assuming you want as great an improvement in sound quality as possible, then I recommend spending as much as you can and buying separates. Todays integrated amps in the $10K price point are getting very good (like the Pass iNT-60), but if you desire in the long run to improve the sound quality buying used separates now are likely to get you better sound and allow smaller incremental purchases later. My rule of thumb is to always invest 2x or more in any particular component if you want an “oh, wow… that is a lot better.”
I would recommend a used Audio Research preamp to be the center of your system. They are tubed and possess the best of both worlds: details, great imaging as well as amazing musicality. I would budget $4K to $5K.
For the amp. There are lots of good choices. I really love tube amps, but high power and tubes cost money. On the other hand, my speakers are about the same sensitivity as yours and I am powering them with 60wpc tube power and the sound is fantastic and can be played louder than I can stand. Maybe, look for a less expensive amp in the mean time until you can afford something like an Audio Research REF, Conrad Johnson or VAC.