There is no real stress on an inboard transom so I guess 3/8" is good enough. I used something a little extra on Gentry, like a metric equivalent a little under 3/8", plus the 1/8" lamination only because I had it spare. It was harder to bend around the curve than 1/4" would have been.
I put the fastenings on Gentry after 2 layers on the sides and 3 layers on the bottom, I think. deep enough to be well hidden but enough thickness for them to have something to hold down.
I think the two designs are similar and hope this helps ease your mind.