The most important thing is you love the sound after the warm up. That is hard to achieve and I wouldn't want to risk losing it by switching components.
The problem seems to be the long warm up and the heat. A "cheap" solution would be to leave the amp on all the time and buy an air conditioner for a couple hundred dollars. Presumably, your listening room has a window for the heat exhaust.
You could leave the amp on all the time with the door closed and turn on the air conditioner half an hour before you want to listen. And of course turn it off while you listen because it's noisy.