UH. That is a huge list I'm sure.
I know I've probably planted at least 15 maybe more than 20 varieties in my AP system just in the past two years. You don't need any special brand or type of seed to plant in aquaponics. I've in the past grown lots of lettuce just suing the seed packets I got at the hardware store. Now days I order most of my seeds from Johnny's Selected Seeds.
I found that Oak Leaf lettuce varieties grow well in warm\hot weather.
We are running 30 varieties right now in the cool water system, and they all work. Red sail seems to be bullet proof. Yet many bibs and are being grown in hot places all summer long.