How to not Consistently Cause Self-Harm

I've always been very good at putting my weight behind my hits, from as young as I can remember when I told myself to punch my body did so in a way I did not have an explanation for until my teen years. Having got a new heavy bag recently, i've been beating away at it, practicing different directional hits and shifting to keep both my hands, head, and waist all moving. Unfortunately, I can't keep from mangling my mitts after only a half hour or so. I use wraps and training gloves, and other than the occasional sloppy wrist-work that comes with no real training and minimal practice, I don't feel the results of my labor until well after. Seeing it, is another matter, as when I remove the gloves and tape i'll consistently have broken blood vessels between all my fingers, dark purple bruises over the knuckles, and in a few particularly bad cases, stiff, clanky movement.

I'm not sure if i'm doing something wrong, if there's a way I should be hitting the bag that i'm ignorant to, but having to spend days, and sometimes weeks, letting my hands recover after only a few sessions hitting really sucks.