You already have a very decent amp & preamp (within your budget range).
Previous posters are correct - look for higher efficiency speakers (i.e. >94 dB/M) .
When I ran a pair of Martin Logan Spires (94 dB/M), I powered them with a pair of monoblocks that put out 900W @ 4Ω. As I’m 64 and have experienced many (many!) live rock concerts from the front row in the 70’s & 80’s, I rarely pushed them to loud levels.
I was constantly asked why I needed 900W, but I would astound my audio friends by how much detail was still present at very low volumes.
I currently run a Coincident Dynamo SE34 MK III tube amp (8W) that feeds a pair of Coherent Audio GR-12’s (96dB). At 2/10 of the volume pot., I can serenade my neighbours 5 houses away. The detail a low volumes isn’t as good as my ML/900W amp combo, but it’s very, very close. The price differential between the two is ML/900W combo - $10,000 vs the Coincident/Coherent at $12,000 (some components were bought used and/or modified by myself). So not a huge cost difference. But still outside of your budget, so ignore what components I have.
In order to be able to continue to listen to all the detail at very low volumes, you need both a) high sensitivity speakers, and b) lots of quality power. Lower sensitivity speaker (like yours) require am immense amount of (quality) power to sound good. What sets a great system apart from a lacking system (at a minimum price point) is how much detail you can still hear at low volumes of sound (aka noise floor).
So, if you’re going to start with one of them, given your budget and current equipment, I’d recommend you start with the speakers.
Consider how much you’ve paid me for this advice and act accordingly...