Looking for a new power amp - choosing between T + A, Atoll, Rogue

Sorry, perhaps I was not clear. You don't purchase based on how much something cost... you buy the very best sounding and compatible component around that price. It is not price driven, more like restricted. When I have assembled systems it is based on sound quality, in the end, the costs have fallen roughly into these categories. My current system is  30% speakers, 20% amp, 15% Preamp 15% DAC, 20% Streamer. 

If you want to optimize your speakers to gain the most out of them then you would want to optimize your whole audio chain. Yes, I think your speakers would benefit from an audiophile amp. Used can get you into that category. So, you don’t have to increase your budget. Most of the stuff I would recommend is over $10K new. It puts you in a place where all aspects of the sound are really well reproduced. 

Then you’ll need to look at your DAC. For long term planning purposes I look at 30% speakers, 20% amp, 20% preamp, 15% DAC and 15% streamer. Having a really solid performing preamp and amp will set you up to get the most out of any input. Of course this is just a generality. I have gone much higher on electronics and got much more out of a pair of speakers than you expect. 

Congratulations on your new speakers. Just checking… but they are broken in? I’d make sure they have a good 200 hours on them and you know what they sound like with your current system before swapping anything.

Assuming you like the sound characteristics of your Audible illusions preamp then I would look to upgrade your power amp. I see you are shopping in the $5k range. That is a difficult price range. It is about half of audiophile products and above budget components. I would consider carefully where you want to go… towards slam / details or musicality. 
 

You can get a used amp at about half price from entry level audiophile equipment.  I would consider a used amp from Pass… an X series if you want slam and details and XA series if you want warmth and musicality. I’m sure there are some other good choices… but this would significantly improve your system.