My grandfather, dad, and I were all electricians, and dad used to wrap our baseball bats with 3M friction tape to give them a good grip. It certainly worked well, but at the end of a game we had to try to get the black gooey residue off our hands! 
I never found friction tape to not stick well to any smooth surface. But it's a real booger to get off, and get the black residue off when you want to remove it.
I use the bicycle inner tubes myself, and not just for front rests. I get different size old tubes from the local bike shop and cut bands from them to use for wood repairs. They work great to hold donor pieces into stocks while the glue dries, and much better than clamping odd shaped surfaces.

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I’ll just say Gaffers Tape. In the yacht business there are hundreds of tape jobs and a large percentage call for duct tape. Cheap duct tape should be illegal. As was said before cheap tape is just that ‘cheap’. No percentage in buying crap tape it costs you more in the long run in failures and clean up. Gaffers are movie set riggers that set up lighting, props, stands you name it  and you’ll spot them by having rolls of tape on their belts. 

Comes in all types colors and textures, low tack, high tack, low stretch high stretch, thick and thin but most will not leave adhesive residue which is a nightmare. I’ve always got four or five rolls in different colors, textures and thicknesses in my shop. If a tape will work then Gaffers tape will do it best. Even if you don’t need it for this project everybody should have a roll or two at the house or shop. 

Rick