If you began with the oil based polyurethane I'd keep using it.
You should never use a latex base over an oil base unless the surface has been prepped. That is sanding it to rough it up, or using a bonding agent. Especially with a gloss finish.
I despise latex finishes in a moist enviornment, only because I am used to marine grade coatings.
Also...try sanding a peeling latex paint finish smooth.
I prefer the oil finishes over water based.I guess I'm patient in that regard. However, I do agree with Chris on one major point. Recoating a couple of years from now. You're looking at a week or more between multiple coats, and off-gassing the finish. You better have an extra enclosure.One possibility is to use a spray polyurethane to reach inside the enclosure when completely assembled. It is of course much easier to brush it on before assembling.When making repairs to the finish, spraying is always possible.
I have used oil based polyurethane to coat the decks of boats, and then covered the deck with carpet, which holds water.
I have never had a deck warp or rot. I do however dry the plywood completely. And use multiple coats.Multiple being sometimes as many as 5 coats.
I have noticed, nobody mentions drying the plywood when talking about cagebuilding.
Use your oil based poly, and sand lightly between coats for a super smooth finish...remember to wipe with a tack cloth before re-coating.
Ok...I've rambled enough.
Bob