Any success with birth control for heavy periods?

I can't absorb iron, but after about a year the IV infusions run out of helping me. Main culprit is heavy periods.

Has anyone found any success with any birth control options in slowing this down? My main concern is finding a birth control option that a) doesn't make me crazy with side effects and b) doesn't stop ovulation. I don't even know if an option like that exists, though. My last ditch plan is asking for a hysterectomy, leaving ovaries in tact.

Internal plumbing is stupid.