Tumble dryers and washing machines use very small drive pulleys with fairly extreme wrap around, spring-loaded adjusters and ony 16-20mm polydrive belts as I recall.
Some domestic machines use a stretchable poly-vee belt & do away with the tensioner. The grooves for the belt are ground directly into the motor shaft & the drum is plain (no grooves), so they operate much as has being suggested for the Kennedy modification.
At my previous employment we modified some of the belt building machines at a belt manufacturer to make the stretchable poly-vee belts for tumble dryers, adding a closed loop tensioner to apply the stretchable cord at a preset tension onto the rubber base layer. Normal belts used a different, non-stretching, cord – Kevlar IIRC. The belt building machines were modified manual Binns & Berry centre lathes that were converted to basic CNC operation, the cord being applied using the screwcutting cycle to get the required cord spacing.
The belts were manufactured as tubes about 2 metres long which, after vulcanising, were slit into the required width belts on another modified lathe that had Stanley knife blades mounted on the toolpost.
The issues I had when designing poly-vee drives were mainly due to the tension required to get them to drive properly without wearing out too quickly. Inadequate tension lead to the flanks of the vees on the belt wearing and, due to the narrowness of the vees, they soon bottomed out in the grooves and slipped. Short centre distances didn't help either, reducing the contact arc on the smaller pulley. High belt tension + plain bushes = likely short bearing life !
The OP's comment about the original belt not being very flexible suggests that it is old. The Kennedy I inherited from my father was incomplete & didn't come with a belt. I mangaged to get a new replacement from the bearing supplier we used at work & my recollection is that it was very flexible. Can't say how it performed, though, as I found one of the Taiwanese 6×4 bandsaws locally in a small ad & refurbished that rather than the Kennedy, which was subsequently sold still incomplete. From memory the replacement flat belt was some sort of plastic compound & was green on the outside & yellow on the driving side.
Nigel B.