Before considerations of "warm", what about things you are sensitive to in a negative sense? SS amps with low measured THD but relatively high levels of odd order harmonics? Hate them.
Tube amps with sloggy, lazy, rotten tomato being hit by a mallet bass? Hate them.
Also any amp that has colorations in one band but not another? Hate them too.
So outside of frightfully expensive tubes - they are out for me (in amps, not pre-amps or DACs). Retubing amps with any sort of top shelf tube gets very expensive as well.
So, first wipe that type of thing off of your list (things you don't liek). Are you keeping your speakers a long time? Good. What do others say works well with them - good way to start a listening list.
Warm? Class A, Class A->AB, fets - I think most of your warm amps that are not tubes will be found to have one or more of these traits. My amp is a Pass X-150, got the A->AB and the right sort of transistors. Clean, fast, of one piece from top to bottom, depth, accurate with a bit of sweetness, lots of current, will drive ML's, Maggies, even Duettas. I found mine, hopefully you'll find yours.