If you can find a GaN or Purify amp that can do 7 channels they’d be well worth a look, but I’d think they’d be above your price target even if you can. D-Sonic has been making well-regarded, high-value amps for years, and you can get their 7-channel amp at 400Wpc for $3375 new direct from manufacturer. There are some favorable reviews online if you take a look.
https://d-sonic.com/amplifiers/
Best of luck.