My factory installed TV (2006 Vista 278) is installed with a wall mount that is screwed to the bulkhead you mentioned. There's plywood between the vinyl and the fibreglass. I can't see any reason for dismantling the bulkhead.
My TV fell down once, the screws pulled out from the plywood. I fixed the problem by using heavier screws. If it happens again I think the solution would be to take down the mirror in the head and make a couple of holes in the fibreglass to get access to the back of the plywood, then cover the holes by replacing the mirror. I could then use nuts and bolts to hold the TV bracket to the plywood.
I hope this is explained properly, if not I would be happy to attach a photo.
Update: Not from my boat but similar...

