What therapies have you found most effective in treating teenagers with recurrent CARP?  

I have found CARP to be uniformly responsive to minocycline. In my experience, the incidence of recurrence is low and normally responds to minocycline.

My preferred medication is doxycycline, which patients also are almost universally responsive to. I do find recurrence rates to be relatively high, though usually not immediate and often not as severe as their initial presentation. I often do keto cream for maintenance with mixed results.