Well........I had done the same thing to our C385. I had misgivings about using an swing arm mount due to the arm/moment in a seaway, so I mounted it flat to the bulkhead, using a standard flat mount. A nice sturdy setup.
I estimate the plywood bulkhead in the main saloon was about 3/8" thick, a 1/4" gap, then on the head side a 1/4" fiberglass bulkhead. We had to remove the vanity in the head to gain access to the nuts for the tv mount and for the cable run. The tv hdmi cable , antenna coax, and 115 ac power are run in the gap between the bulkhead to the main electrical/ electronics panel. We use a Fusion Av 750 deck.
The ac power cable is run to a dedicated pure sinewave inverter for movies at anchor.
As far as determining the overall bulkhead thickness, i would use a very small drill bit and drill an exploratory hole at the approximate center of the proposed tv mount, being mindful of electric and water lines. If the medicine cabinet is behind the proposed location of the mount, remove it first.