1. Procure a quality heat gun. If you're going stapleless, then you need the wood to conform to the correct/desired shape without a lot of force holding it there. A heat gun will allow you to curve/twist the strips so that they almost just sit there by themselves.

2. Resist the temptation to start smoothing and fairing before you're finished stripping. Once you start, it's hard to stop, and you have to be extremely careful thereafter not to ding or scratch your sanded timber.

I used 'bunch of those little wooden pieces' to hold my first strip while the hot glue went hard.

Have you decided the 'bead and cove' or 'rolling bevel' question yet? A slight tweak to 'those little wooden pieces' can make beveling really easy.