Go to an automotive parts jobber and request belt non-slip spray. The stuff comes in either a spray or a bottle. It will likely help. Also, if the leather has stretched but is otherwise in good condition, you can try soaking it and then drying it (use oven at 150 degrees for 5 minutes and then turn oven off and allow belt to remain in warm oven). Afterward, however, you will have to oil the belt with something like neatsfoot oil or WD-40. This process may or may not stiffen and damage the belt. Usually it works out fine, but sometimes it doesn't.
Also, try sparingly lubricating the bearings of the tuning devices. Ball bearings should be packed with a small amount of light grease (Vasoline would work well, though a high temp. wheel bearing grease is better with the heat of the tubes). All other bearing surfaces should be lubricated with a drop of engine or 3 in 1 oil.
Thomas