As a quasi-professional, I have to advise you to use extreme caution when heating vintage wraps with a heat gun. Keep a bucket of water handy, and immediately turn your heat gun away if you see the slightest hint of flames. They are extremely flammable, and they will burst into flames almost without warning. I unwrap all drums outside, where I wear goggles and a respirator, since the fumes are toxic.
If you're going to rewrap, don't go with that Jammin Sam tape ****. First of all, "Jammin" Sam Barnard is a ******bag, and second, taping your drums is cheap and the wrap will never "bond" with the shell properly. Use 3M NF30 Contact Cement and you'll get as good a job or better than the factory did, especially if you cut the sheets yourself and file at the bearing edge.