Penetrating epoxy is excellent for this purpose. You can paint
it on, or pour it on and spread it around with a plastic putty knife. Especially in the known vulnerable areas, like in front of the door for instance. This material has the consistency of water and will soak in to harden and waterproof the surface. Since it is so thin, it will soak in, wick and travel along under bulkheads or the threshold. Getting it into tight areas should not be much of a problem as you can simply reach in and pour it out of a Dixie cup. Then spread it a bit with the putty knife, or brush it a bit to get it everywhere. It is thinner than paint
, soaks in and takes hours to harden.
Out in the general areas, it will give a harder, cleaner surface that will accept glue or sticky-back finish materials much better than simply sticking them to old plywood that can have embedded dirt or weak fibers.
There are also a number of materials that are spread over plywood and tile backer board in showers. These waterproof and prepare the surface to accept glued materials. Home Depot should have a few selections of these, but they will not soak in as well as penetrating epoxy.