Well ...This is a 2-part question at least.
First, you get a bunch of difference forces piling up on the transom. For example, every time the boat flexes (oil-canning and hogging), the transom corners try to flex as well. Those corners are stress concentraters. To fight that and to prevent breakage of the epoxy fillet and glass at those corners, you want to build strong fillets (see the construction manual on this) ...but you also want a stiff transom. So even though your motor will be out on a hull extension, this boat flex will be occurring regardless. I vote for a strong transom, your 'rear bulkhead' above, and would go 1" thick from the deck up.
The motor, especially on an extension, will throw it's weight and thrust around and try to impart racking (twisting) forces on the transom. Part of that will also impact the transom (your 'rear bulkhead') ...I would go ahead and go with 1" thick down to the bottom panels.
The Proverbial Bottom Line: I vote for a 1" thick transom from sheer to fairbody...
For the minor weight increase compared to going lighter, I would encourage building a little stronger as spelled out above for boats like yours that have an extended hull (which I like better than an Armstrong type bracket for example).
Brian