Hysterosalpingography (hsg) worries--is that stuff they inject safe? What about xrays of ovaries?

Safe contrast & Only use small amount of x-rays to be safe. See radiologyinfo. Org.
Yes. The contrast - 'stuff' - used nowadays is sterile, non-toxic, and washes out with water; it is very safe except possibly to women with iodine sensitivity. The amount of x-ray exposure to the ovaries, even in a lengthy study is still way below the allowed safe radiation limits for gonads. The procedure is kept as brief as possible, while still getting the needed information.