Maybe I'm thinking of different modules. The ones I think you are talking about are like 20mm with 3 of 219's. Do the emitter on the modules line up with the reflector holes? I see. You intend to use the whole modules, optics and all
With King Kongs, I don't see you getting much over 1.4 amps per emitter on high. That is also RMM's experience reported here. My build in that same thread linked had 4P 18650's feeding 4P emitters. I didn't even need to put them on copper bases. Your case will be 3S1P KK feeding 3S3P modules. So you should have even more voltage sag and less current.
Not sure if 3 emitters on a 20mm aluminum base is OK at 1.4 amps per emitter. My guess is they will be fine, but I wouldn't rely on my guess.