@Bennet,
Thanks, Bennet.
No, sweat hasn't been a problem; it's more a matter of having worn through the original material. Leather could be good, but the last wheel cover I had was too bulky when installed, and was a kind of sloppy and loose fit. I couldn't stand to feel it move around under my hand, and honestly, while I could afford such if it worked, it might be another expensive experiment.
Tennis racket grips have big potential. The start of the wrap is not problem, but they are usually terminated with what amounts to a big, fat rubber band. I don't know if I'm crafty enough to make a solid termination or not. I may go that route and find out. That reminds me of baseball bat grips, and the bar tape they use on the handlebars of road bikes. This ups the cost considerably, but well worth it if it works.
Thanks, you've kind of stimulated the thought processes.