You might be surprised at just how much the little cogged belts can take. They are thin enough to hold the strands that give them their strength, but not so thick that heat build-up becomes an issue. If you cut a Vee-belt apart sometime, you'll see that the strands that give them their strength are no thicker than the cogged belt. They need the thickness to give them traction on the sides of the sheaves, but the thickness comes at the cost of heat build up when they run. A Vee also slips and rubs a bit when running, so they will wear faster than the cogged belt too.
Just the same, I ordered spare belts for my lathe. Got the Vees, but the cogged is also on back-order. Have you checked with Lathemaster to see if they have the belts?