I’m a treadle-user, fairly frequently as a matter of fact, and I want to point out that the pulleys on treadle machine heads and stands are designed to take certain sizes of round belting specifically to increase the grip and minimize the drag caused by the belt. Fatigue is a major consideration with about anything manually operated by a belt, and especially a sewing machine.
If a treadle sewing machine is actually going to be used frequently for sewing, the appropriate size and type of belting should be an important consideration. Most home sewing machines are designed to use 3/16” diameter leather belting (no plastic back then). Most “artisan” semi-industrial sewing machines have pulleys designed for 1/4” round leather belting (Singer 31-15 and such). The belting size provides the most grip with the least drag, and that’s what you want. Leather belting flexes appropriately around the pulleys, too.
The pulleys are designed to have the belt grip the pulley along both sides of the pulleys, not down in the bottom of the groove. That’s why using a small string to measure a machine for a new belt isn’t very practical. The small string lies down in the bottom of the groove instead of up on the sides of the pulley where a belt should run. By running up on the sides of the pulleys, and having belt grip of the pulley on both sides of the belt, the belt can be run much looser, reducing drag. A tight belt increases drag. When you find it necessary to measure for a new belt with a thin string, allow plenty of extra length for the belt to ride up on the sides of the pulleys.
Using plastic tubing, continuous springs, and even clothesline cord will work for sporadic operation of a treadle sewing machine, but they can be a drag for continuous use. While I don’t have much experience with plastic tubing (my tubing experience was a failure too, Joe), or springs (haven’t ever tried one), I have had good luck with round leather belting. A clothesline cord joined together with masking tape worked just fine on a boot patcher machine that was used mostly by hand cranking it for repairs (didn’t use the treadle to make long runs anyway), and a continuous spring is probably great for swapping machine heads in and out of a treadle stand for test-sewing (spring tension increases drag?), but I always go with leather when I’m going to be actually sewing for real on my treadles.
To answer the OP question, I usually replace every leather treadle belt with a new leather belt when I rehab an old machine for use. Rot and stiffness is the thing to look for with an old belt. If it has rot, it will probably break. If it’s stiff, it increases drag. New leather belting is available, so use the good stuff on your treadle.
CD in Oklahoma