You put wood, as in tree/plant material, on a styrene kit?
I think you need someone better skilled than I, but I'll take a swing here...
Seal the wood bits with a primer like Floquil for trains, or any strong/durable filling primer. That way they'll have a sealed surface which can be mated to the plastic parts with more common methods, I'm thinking CA.
That said, I'd love to see your GT500, my other hobby is a 1:1 functional model. Not a real Shelby, not even close (a mere "C-code" which they made many many thousand), they made no convertibles in 1967, those came out in '68.
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