Is there really a single right way to carry a camera underwater? I dive with a variety of seasoned dive photographers, and they all do it differently. I say carry it in a manner that works for you, and you'll be doing it the right way.
I do it all kine ways, depending on the situation. I know the original post was regarding muck diving, but here's what I do in various dive scenarios.
Shore Diving:
I carry mine to the beach using two short hand-braided lanyards on each side attached to my D-rings. If one lanyard fails, the other lanyard will still prevent my rig from dropping to the ground. Once in the water, I detach both lanyards and carry it...sometimes with one hand, sometimes with both hands.
Offshore:
If I'm offshore, I keep it connected with a short hand lanyard. No BCD, so no D-rings. No strobe arms for this scenario.
Blackwater:
On Blackwater, I use my D-ring lanyards when first jumping in, then switch to a short hand lanyard
Boat Diving:
I leave my camera attached to to my D-ring lanyards when first jumping in, then detach and adjust strobe arms and remove the dome port cover. When ascending, I attach to my D-ring lanyards for safety stop and/or SMB deployment.