I believe a fair number, if not most users, are mounting these pedals (the Stomp and Stomp XL) on pedalboards and are powering them with various power supply bricks. I use the Cioks DC7 to power mine, and it works great. I suppose if I were using a wall wart type supply and needed a replacement, I’d look for something that meets the specs that less money. There are a bunch of third party power supplies available on Amazon and other places. You just have to make sure they’re the correct voltage, polarity and are using the proper plug size.
The older Line 6 power supplies you mentioned are actually 9V AC, so you’re correct, they won’t work with the XL.