Re: Transom out of 2 3/4" pieces of plywood.
I would recommend you paint the ply pieces with resin until they take no more, usually 2-3 coats and it only takes a few minutes. Then layer them in a jig or use SS screws yeah any screw really, and get them fit together as fits in the boat. Then lay glass/resin and put it together with screws or weight it down to compress them together some so you have no voids. The glass between will divide the wood core in to sections as well as add strength to the composite panel you are building. Put all the layers together within the time allowed for a wet bond, IIRC with epoxy it is 24hr you don't have to sand and get a chemical bond not just mechanical. I do sand a little to smooth parts off. When you get it all done put it in the hull in one piece, it will be amazingly strong. Don't forget to seal any and all holes you put in it.
If you put layers of glass between it will be much stronger than just the wood, that is a composite even though the wood core is also structural. Remember glass makes it strong the resin is just glue that holds it there and weak in its own, but it will waterproof the wood if you soak it before installing.
Some performance boats use 1/2 ply, and they use marine ply, to make some of the strongest transoms. For most normal boats two layers of CDX 3/4 will do just fine and add in thinner to get thickness of what you need. For a performance boat with high speeds/HP I'd be more picky how I did it.
I prefer epoxy but you don't have to use that type of resin. You will have to make clamps to hold the wood tight to the existing skin of transom to get a good bond in there. Many use mat or cloth, it holds more resin so you keep the voids out better when you are bonding two parts together like that that may not be perfect or are flexable.
So wet down one side of the transom and then let is get close to hardening then lay down one layer of csm then wet that down then wet down the other piece of wood and clamp or screw them together?
Most build the entire thing, then drop it into the hull with glass (mat/csm/etc; whatever you want to use) on it wet and clamp it up to bond it back to the skin. Some even paint resin on the skin so it has a fresh coat to bond to, I'd do what the resin maker recommends. Never let it kick part way for anything I can think of. You never want more resin you want to squeeze it out. Resin is extra weight and without lots of glass in it, it is very weak and can break. I have left glass stuffed in voids and poured resin inside there later, otherwise I'd never use more than I had to. If water got into a small void down the side of your new transom for example, it might get into the wood any place on the end of it. Last one I did I drilled a hole and poured it full there, but the gap was pretty small anyway.