For that matter, you could always go full Munchausen, and make yourself genuinely sick or weak.
But being stuck in BCT for endless cycle after cycle seems like a special kind of hell.
E.g., you change your mind about joining the military. You can't resign or run away, so your best option might be to convince them that you're more trouble than you're worth.
In other words, if you actively want everyone around you to think you're an incompetent fool, then deliberately washing out of boot camp is the sort of thing you might try. I don't see why it wouldn't work. Refusing to accept the training would get you court-martialed, but you can't charge someone with just being a lousy shot, can you?
You really are trapped, and the only way out is even more painful or results in a criminal record. That was my experience, us army 98 to 02