Ahhh, got it. You're right, the bulkhead can have had no effect on supporting the house. I would not count that deck 'beam' as much help in supporting anything, either. It's too small, not deep, and not made of anything particularly good. There's just not much chop there and few fibers in the chop would be going the right direction. I think the original designer's belief was that the entirety of the deck-house-house/top moulding, with its cored flat surfaces, was plenty good enough with the few stiffeners.
So, where to go?
Posts would be fine; they'd have to be standing on something good, like hull stringers (rather than floor, unless the floor was well supported on the stringers). I suppose they'd be a total of about 4' tall. 1 1/2" x 1 1/2" and 2" x 2" is pretty small (Euler's theory and the radius of gyration...don't ask, I don't remember). 2 1/2" x 2 1/2" would be more than adequate.
Knees would be problematical unless the hull was quite stiff or reinforced.
Plywood casework would be dandy if well thought out and supported and carrying the corner of the house.
A new beam in place of or alongside the existing would be dandy. You'd want to cut any stiffeners that the beam would cross so that the beam could be up against the deck (to reduce its obtrusiveness), then you'd tab the cut stiffeners onto the sides of the beam. The deck will have curvature so your new beam would as well. You could laminate it in place - gluing and propping each lamina up. The lamina could be 3/4" thick and as wide as the engineer says - my guess would be 2 1/2". And the thing would be stacked up (down) to be, say, 4 1/2" deep - 6 lamina. Again my guess. 12' is a long span. You'd have to tab the thing quite thickly to support the ends on the hull.