I have stripped some inlay work on my deck that must be at least ten inches long at the widest and completely unsupported by any forms underneath. I found that flat-edged strips (no cove or bead), well fitted to the surrounding wood, stayed in place well with just the adhesion the wet glue provides. The idea of putting contact paper underneath sounds like a great back-up and should make your process even easier. A small piece of duct tape, on the inside or outside connecting the new strip to the surrounding wood, should do the same trick. A roll of duct tape is worth a dozen clamps. I hope it all turns out well!

Mike Johnson