You might want to try mastic gum. It has been shown in studies to be at least as effective as abx for treating h. pylori.
I've seen it mentioned. But does the same question arise as with limonene? Am I going to screw up my other microbes by taking an anti-bacterial (I think that's what it is)?
I think I was mistaken in thinking that d-limonene is necessarily anti-bacterial. Its mechanism of action doesn't appear to be known (not convinced I'm searching well):