I might be reading this wrong, but from the OP's description of the project- "bent wood" and "thin strips", the design could involve bent wood laminations. If so, and springback is a concern, than neither PVA (Titebond) or urethane (Gorilla) glues are good options, since they allow considerable joint creep (and therefore springback).
I'd recommend using a resorcinol glue, such as DAP Weldwood Resin glue- no springback, long pot life (esp. good for lamination builds), strong, and water resistant. I've used it on several lamination projects, and don't find it hard to mix or work with, and it gives great results. It does need fairly good matching surfaces for maximum strength, though.