I would seriously advise you against making changes to your regimen based on internet avice if you feel good. If you feel fine injecting twice a month, I woul just continue like that. Lots of people will say, based on broscience, that you cannot possibly do that, but how you feel is the most important.
Have you been to a good dermatologist for the acne or just your GP? There are several other possible therapies besides the doxy and the accutane that you don’t appear to have tried.
I’ve been to two dermatologists. The first one refused to prescribe me accutane because she feared it would aggravate my crohn’s (which it has not at all). I tried various topicals including topical antibiotics (sulfur based too), benzyl peroxide, soaking in epsom salt baths daily, and Doxy at 200 mg / daily before I went to a derm. in my hometown who prescribed me accutane. I’ve definitely exhausted my options, I just didn’t mention them because they had little to no effect in treating my acne.