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G'day Roger,
How thick is the plywood? I'm surprised it would warp at all.
As for your solid timber pieces, timber expands and contracts across the grain. So long as your pine pieces are relatively narrow (40-60mm) that shouldn't really be a problem. However, when you screw the plywood to it, make the holes in the pine oversize, since the pine will try and move but the plywood won't. If you don't let it move, it will crack somewhere.
You can paint straight over the timber if it's just for general use.
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