Belt dressings are sticky and will grip the belt  but this creates heat.  Slipping also creates heat.  

Use castor oil on the belts, if you have belt slippage. Belts run cooler and don't pull apart.

An old timer told my dad to put castor oil on the belts on a Papec silage cutter.  Daddy put belt dressing on some new belts and they pulled apart.  When he switched to castor oil, no more belt slippage and the belts lasted.

A good source of V-belts is JayDee Enterprises.   https://www.jdv-belts.com/products.htm" rel="nofollow - https://www.jdv-belts.com/products.htm

The problem we experienced (and I'm guessing your problem too) is that most belts with kevlar/aramid cords typically also have a much stiffer section. The belt manufacturers do this so the rest of the belt can handle the increased tensile and breaking strength that the kevlar cords allow. This causes them to need much larger wrap radii, and they'll get brittle/crack/slip if used around smaller pulleys. The bending and cracking you describe is exactly what you see in these cases. If your mower originally had basic nylon-cord belts, there's a good chance the pulleys/sheaves are too small for standard kevlar-cord belts. When this is the case, they also need to be uncommonly tight to not slip, because the stiff section doesn't grip down in the smaller sheaves nearly as well. That may explain why yours are getting so hot. I don't have my belt tables in front of me nor know what size of belts you have, but I'd guess a B, C, or 5V section. In which case, if using full-section kevlar belts, your pulleys probably need to be around 8" diameter at the very least to effectively transmit power and not crack or slip. If you go to cogged belts, you'll probably be ok down to 4" or 5" pulleys.

Try cogged ('X-series') belts and I suspect your problems will go away. Cogged belts also help keep the sheave groove from getting packed with crapulence - which is why we use them on sawmill equipment at my current job. And make sure you're getting the right series of belts too: It's a pretty common mistake to put conventional (A/B/C) belts on sheaves meant for narrow-section (3V, 5V, 8V) belts (or vice-versa), and they won't grip right and cause grief.

In summary: I strongly suggest sticking with kevlar, but using cogged ('X') belts. If possible, find good quality ones (sounds like you already are if you're using Gates. But Gates also has several different styles of kevlar belts with different properties for different applications). Make sure you have the correct section (ex. 5V vs. B - the pulleys may look identical, but they'll cause all sorts of grief if the wrong one is used). I suspect you'll find your problems solved if you do all this. If your pulleys have seen a lot of slipping (sounds like they have, judging by how hot they're getting) it won't hurt to de-glaze and inspect the grooves to make sure they're not worn such that the belt section isn't sitting in them improperly.

I can't imagine any scenario where a nylon belt would outlast the correct kevlar belt.