I have read journals which say accutane is the only full proof way to get rid of it at 0.5mg per kg
The thing is, I have already done a course of accutane and while they all went, they came back after 4 years of finishing treatment.
BP is effective but it destroys the skin and when you stop the pustules do more damage to the compromised skin
Antibiotics work while you take them, as soon as you come off you get more with a compromised gut, the same for topicals
Do I really need to take the tane again, FML
Suggestion: Try diet as a way of hitting this from the root. Keto or Carnivore diet should help. And...add in supps. Up to 6 fish oil pills per day, 50mg of zinc gluconate, and make sure your vitamin D levels are good (you can get a blood test for it).
Since you've already tried accutane and don't want to again (which I don't blame you), if you have the motivation, targeting acne from the root through anti-inflammatory diet and supps could do the trick.
If you try it, I'd be curious to hear how it goes.