I just wanted to let you know that my DX is Hypothalamic Amenorrhea (HA), which it sounds like is what your DX could be as well. I did have success twice with IUIs but had to use injectible medications. An IUI cycle with injectibles is more expensive than an IUI cycle with a pill like Clomid, but is still way cheaper than IVF. I unfortunately, lost both of those pregnancies but neither loss was related to the HA.
Good luck and make sure that you are discussing all options with your RE before just moving straight to IVF. If your RE is unwilling to try or even discuss a cycle or two of IUI, I would seek a second opinion.