The one thing I am thinking is that I would need to be using nails for false deck to make the correct curve as PVA wouldn’t be enough. And it means that nails should go before planking. Thinking out load to bounce some ideas.
Dont try fighting a flat false deck by trying to force it to bend. It's a real pain to hold a springy deck down. The glue joints will not be strong if gaps are present. You should give yourself as many advantages as possible so you don't have to force the false deck to into shape while trying to glue it to the curved edges of the bulkheads.
Precurve the fals deck by soaking it in water for a half hour, then place it against the curved suface of a large coffee can or small bucket or similar object to act as a form. Use rubber bands, lots of them, to hold the false deck to the curved surface of the form and let it dry overnight. The next day, the false deck will be curved to shape. When removed from the form, the false deck will spring back and loose a bit of its curvature, but should have enough curve left to fit will to the ships frame. If not, curve the deck on a form that has a smaller radius and attempt to pre-curve the wood again. The curvature of the wood may still be either a bit too shallow or too deep when fitted, but a lot of the force required to make it fit properly to the bulkhead edges will no longer be required. If the deck is not planked, you can use fine pins to pin it to the bulkheads. You can also use LOTS of rubber bands wrapped around the entire model to hold wooden blocks, or better yet Legos, which in turn press the deck to the curved bulkhead edges while the glue dries. When rubber bands and blocks are not practical, your can use weights to hold the deck down. I have calibrated steel blocks which make good weights.
After the glue dried, you can either remove the pins (if used) or pound them in a bit deeper to submerged their heads into the false deck and leave them there, and plank over them later.
Curved beams were installed to provide camber (thwartship curvature) to the deck. Here you can see a pre-curved false deck about to be glued in position and held there by either pins, blocks and rubber bands, or weights, or a combination of any of these.
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