What kind of material are you planning on using for this? Sometimes material choice will make a huge difference and allow you to use one solid piece. Like in LAFENGAS’ DIY thread.
Obviously the challenge is reducing the residual forces from pushing the material to the shape of the plastic, so if the material stretches enough, it will reduce those forces alot. The vynil you had on there, probably doesn’t stretch much at all compared to alternatives.
Also, if you already had a 3-pce section of material, and it didn’t stick, that’s because the shape probably wasn’t proper. If you modify the template to fit better, there should not be a problem.