Hey Another Brian, I like your handle! You could also go by Brian #3. har
As for nets, you have a good point, a net with a big mesh will rip apart the tails of the halibut. Fine mesh nets are hard to find too, so I understand your dilemma.
My strategy out there is to only net fish that I believe are really truly legal. I have been wrong a couple times and netted 21.5 inch fish. That's a bummer but it happens.
Halibut are a tricky fish to handle but I have had good luck grabbing the leadhead by the head and pinning the flatibut against the side of my tube. Then I put one hand over it to hold it still and I pop the hook out after grabbing my pliers with my other hand. A tricky move, but effective.
Along those same lines, with whiteseabass the best way to grab sub-legal fish is in front of their dorsal (top) fin but behind the gills. Don't touch the gills just grab them right behind the gills from the top. Saw some deckhands do this once and it works well.