Howdy and welcome to the forums!
As the one maintaining the Savage Rifts files I have to agree that the Mystic is quite broken.
A large part is, as you’ve seen, due to the limitation of a single Arcane Background per hero. I had tried to create a “Secondary” AB for the Mystic and the Dragon Hatchling, but not sure they’re working as intended (I think you’re the first to try the Mystic and mention the issues.
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Hopefully, this will resolve somewhat when the next update comes along allowing for multiple AB per hero. Hopefully it won’t take long to get that back-coded into the Mystic.
I’ll look into what you mention though and see if it’s an easy fix. What version of the SR files are you using?