I have one of these in a second system and it would have no issues driving your speakers. Definitely a warm sound and built like a tank. The footprint is more than 7 inches. Did you mean height? That's less than 7 inches.
https://www.ebay.com/itm/Cary-Audio-Design-SLI-80-w-remote-excellent-used-cond-Audiophile-NOS-KT-88s/113717852483?hash=item1a7a1cb943:g:DCAAAOSwpa5cYfSG
https://www.ebay.com/itm/Cary-Audio-Design-SLI-80-w-remote-excellent-used-cond-Audiophile-NOS-KT-88s/113717852483?hash=item1a7a1cb943:g:DCAAAOSwpa5cYfSG