As an avid fisher its always intresting to see what the experts say. In commercial halibut fisherys it seema like there is a reason to lay the fish on deck or in a heap with the under side up. generally sport fish and commercial catch are bled quickly/effieciently and then cleaned or iced asap.
Seems like the brown/upper will discolor and blot/ mold to whatever it touches. The white bottom side seems to be more firm, and generally stays the same color when stored, iced , frozen.......
Just wondering? :cf
https://youtu.be/0EneQP1R6nw
Without knowing a damn thing about your fishery, and not knowing much about a halibut other than similarity to flounder, my assumption is in nature their "brown side" is just about never the side in contact with the ground. The other side likely firmed up by evolution. But in general I don't think there's any fish that shouldn't be bled and iced asap. Frankly i wanna filet them asap.... but I fish from shore a lot. maybe not in rough seas.
I believe any fish stored in overly tight conditions for an extended period will bruise. I used to get crushed ice from a fish house and it worked so much better than bagged ice. It was 3 bucks per cooler no matter what size....shovel it yourself.