Don't know if this helps but I always pull the fish lightly through the water to get it on its side. Then I let the points of his dorsal sort of stick into my hand and use that to flip him upside down. This way he will lay in your hand without touching the sides, and they are much more relaxed (or goofy) upside down.
Using barbless hooks usually means I never have to pick them up anyway. THey kinda release themselves.
"even Jesus had a 12 man recon team"