Need a new amplifier. Need a good match for my Audio Research LS7 preamp

To compound the issue, the ARC LS7 is inherently brighter and livelier.  I know, I had one.  That's what was so enjoyable about it.  However, it needs to be mated to a warm amp.  The Muse as timlub mentioned would be great if you can find one.  An older Classe, as mentioned, or Belles amp would work really well.  Try some MIT or Transparent cables as well.  Best.....

Beware that the LS7 needs a poweramp with at least an input impedance of 60 kOhm , normally a tube poweramp has 100kOhm , just look at the specs of the ARC tube poweramps .

If buying used is an option, the older McIntosh SS amps may give you the sound you're looking for within your budget.

Are you planning on upgrading speakers anytime in the near future? If so I’d do that first rather than trying to tame the sound with an amp that may be too warm sounding if you get better speakers later.

That said, there’s a nice Classe CA300 for sale a little above your current price target that should tame the top end a bit along with providing a big boost in power for higher volume listening. There’s also a McCormack DNA1 with Steve’s silver upgrade mods at a bit under your price target. Not a warm sounding amp -- more neutral IME -- but should provide significantly more refinement to your top octaves versus the Arcam and may well also help with dynamics and separation (i.e. less congestion) at higher volumes. This is also an amp that you could pair with much better speakers in the future and still be more than fine, or you could even upgrade amp to one of Steve’s higher levels if you want even more.

Anyway, hope this helps and best of luck.

@hansk46 .....very good point.  IIRC that would rule out the Muse.  Belles and Classe still viable options.  soix's McCormack recommendation is even better imo as you do get a more refined and neutral amp with the correct input impedance.  The McCormack is an amp that can be partnered with many different speakers.

Also IIRC, the ARC LS7 has a higher than average gain ( at least mine did ) which could be contributing to more glare and brightness especially at higher volume.

Best and keep us posted.