"I know that birth control is deeply disordered … "
If you have an option to take hormone treatments which come in the form of birth control pills and, as a Catholic, you are not pulling a fast one and using the pills FOR birth control, then its use certainly could not be considered “disordered” even by the Magisterium.
If the Church would require you to have a hysterectomy instead of taking the completely less-invasive, less-traumatic, less-life-altering birth control pill to control dangerous and debilitating bleeding, what would that say about dogma?
Precisely.
Something that is often overlooked in these kinds of threads is that birth control pills are not intrinsically evil of themselves. They are a thing, a tool, if you will. Objects aren’t evil.
A similar example is this: a scalpel can be used in aborting a child. It can also be used to perform life-saving surgery. Just because it can be used to abort a baby doesn’t mean it’s evil. It’s a tool which can be used for good or bad purposes; it itself is morally neutral.
Likewise, birth control pills can be used for the wrong reasons, and they can be used for the right reasons. If using them can save a woman’s life or improve a medical condition, then they’re being used for good reasons. The unintended consequence of contraception is not a sin. A couple might not be comfortable with that unintended consequence, and may choose to abstain during the time that the wife is on the pill, but they aren’t required to.
The same is true of hysterectomies.
OP, get a second opinion from another doctor if you wish. Personally, unless I knew a doctor who recommended drastic treatment well, I’d probably get a second opinion if I had a drastic treatment recommended to me just on principle, whatever that treatment might be. However, if a hysterectomy or birth control are the best treatments for your condition, please use whichever is medically best for you. I understand that this may make you very sad, and hope you can work through the grieving process with whatever help is best for you. The important thing here, though, is a) that you not sin (and we’ve already shown that either treatment isn’t sinful) and b) that you take care of yourself and your children.