In the original question, Brad's Dad asked what the amber material on the edges might be. Without seeing it, it's hard to tell but I would guess the previous owner used epoxy to try to seal the edges of the plywood. Take a power sander to a bit of it. If its epoxy, it will smell kind of sweet and aromatic.
I like the idea of Line-X. It is very tough. A lot of offroad vehicle restores spray the underside and inside of vehicles with the stuff in off-frame rebuilds. However, it goes on hot (about 170 dg I think) which may blister the original paint. I would talk to a reputable Line-X installer first. It might be wise to remove the original paint before installing Line-X but check with the pros.
If you are going to use paint, I would recommend a good epoxy sealer first. I've use Industrial Formulators S-1 sealer
(now part of System Three) for years and it works great.It soaks in and hardens forming a waterproof barrier. The finish coat could be anything but a good marine enamel or polyurethane would probably be best. Again the epoxy sealer would only work properly if you went down to bare wood but this is always a good idea anyway.