Hi, Barry,
I'm definitely not an expert in this area but, I would use
a good polyurethane. Probably Helmsman Spar Polyurethane.
It is good enough for exterior use.
A friend of mine uses that when he makes signs that still have
the bark on the outside edges and the Helmsman definitely helps
keep the bark from falling off.
I have no affiliation with thier company but, just think it is a good product.
God Bless! Spirithorse
By the way, your idea about adding the plywood sounds like a good idea to me
and I would use the same polyurethane finish on that.