You could up salt dosage to 2 tsp per gallon. A little more extreme and uncommon but you could also try sterilising the affected areas with hydrogen peroxide, using that plus the salt let my female with fin rot start to heal within a few days. A better antibiotic would be another option but I’m not familiar with different types.

Your water parameters are fine, yes?

Bettas are very vulnerable fish, IMO. It's odd, because they're also nearly indestructable--until they get these mystery illnesses, which IME no one else in the tank will get. I lost all my female bettas at 1 year or so, one by one, due to a mystery thing that only got the bettas (leaving the rest of the tank untouched), and was completely incurable despite kanaplex, furan 2, you name it.

All I can do is confirm I shared your experience. And I'm frankly scared to get bettas, even from breeders, now, even though they are my first love among fishes. Anyone know anything more about this mystery betta illness business?

Edit: To treat this, move your betta into a new hospital tank. Completely nuke his normal tank: bleach, then wiping down with rubbing alcohol, then thorough rinsing. Boil the gravel and destroy the plants. Clean your heater and filter thoroughly and throw out the media. Start a cycle again. When it's cycled, add back in betta boy, giving him a good stop in a salt bath on the way back. --But really, this is very onerous, frustrating, and expensive (plants!), and a lot of owners only find it worth it if they lose multiple individuals purchased at different times in that same tank. Otherwise, it could just be that one fish or batch of fish, and not necessarily something in the tank.