I haven't built a Uncle Johns , Jon Boat (as of yet , have the plans here at the house) and from looking at them I would go with the 3/8ths , but that is just me. Then glass the bottom and sides on both the outside and inside. Some graphite and epoxy mix on the bottom would not hurt anything. The outside of the bottom ...not on the inside.
Running that large of a motor I would add three elbows to the transom to help stiffen it and distribute the force (And weight) it will put on the boat.
A elbow is nothing more the a "J" shaped of wood running up the transom and out about the same distance on the interior of the bottom of the boat. It is something they do to boats which are light weight and with large motors. My last , powered, fishing boat had that arraignment but it was made for racing and I converted it over to a fishing boat.
I am not sure if I understand your statement about the weight distribution .... when your boat will be sitting in the water it will be a little heavy on the stern with that motor on it but running it should level out and then if you are fishing from the bow it would level out with your weight forward.
It would pay you to send John a e-mail about this , he is semi retired now but is handling all of the technical questions .... Tell him you have posted the question over here and I asked you to bounce this off him.
It is best to ask a lot of questions before making the boat then to make a mistake and find out about it later.
Chuck.
PS. Tell John HI for me.

By the way I forgot to tell you.... If you epoxy saturate the wood it multiples the strength of the wood up to four times the original strength.