Controlling your up and down hormones may help more than sporadic antibiotics. Leaky gut is vague, unproven, with different folks finding out (after dieting) it has done nothing or their interventions actually remove something causing their acne which had nothing do with the mysterious leaky gut syndrome that everyone claims. Multiple food intolerance and metabolic disorders can result in the same thing.
I have seen one person finding out they needed more digestive enzymes the next finding out that eating high inflammatory foods exacerbated their acne.
I do not know where to start. But I just do not think leaky gut is something you should put your energy in when all your symptoms relate to endocrine function, and sex hormones. Simple solution for some has been birth control while others is exercise and low glycemic, inflammatory foods, and an upbeat attitude.