Cloth/Fabric Tape

Skinning Foam
Excellent
Securing Covers
Excellent
Bridging Foam Seams
Great
Reinforcing Stab Tips
Good*
Handle Wrap
Good
Fabric tapes come in many forms, from medical to athletic tape. It is important for our needs that the tape be relatively soft, strong, and have good adhesion. The less stretch the tape has, the better. Most medical and athletic tapes either don't stick well, or have more stretch than would be desired. There are fiberglass reinforced cloth tapes, like Leukotape-P, that are essentially cloth-backed strapping tape, but unfortunately it proved to not stay adhered when laid down in tension.
Hockey Tape

By far the best option that has been found so far is cloth hockey tape. Each brand is slightly different, but Howie's has proven to be hands down the best that is easily accessible for regular consumers to purchase. Renfrew and other brands are still viable, especially if you aren't taping a space that needs the extra softness that Howie's provides.
Sources
Howie's Hockey Tape
Dick's Sporting Goods
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