A basic principle of wood frame construction is "never use one big piece of wood when two smaller ones will do." One reason for this is that it's easier to carry 2x12s around the job site that it is to carry 4x12s. But the other is that wood in large sections will warp and there is little to resist that force. Two smaller sections may warp but usually not in the same direction.

I've had poor results with laminating plywood; it's quite stiff on edge, i.e., it dosen't sag, but its quite flexible along the face surfaces. Thats why the box beam internal strongback works well--sections of plywood are at right angles to each other.

Personally, I went the route of building a strongback from many small pieces of wood. It's all 1x4s from the lumberyard, a few scarf joints, no table saw required. Picture below if I can figure out how to post it!

Mike Scarborough
Friendship Kayak