Coverage of the elemental formulas by insurance varies by state. My state doesn't mandate coverage of it, therefore they're not covered. While debating this on the phone with the insurance company, I told the lady, "Look, this food is medically necessary and available by prescription only. If I don't give it to her, and give her the H/A formula she reacts to instead, she requires hospitalization, IV, etc. etc. - you'll cover that though, right?" And, yes, they would cover that.
Definitely keep up the TED while contemplating the Neocate. Back when dd1 was on Neocate, it cost us $36 every other day. That adds up really quickly; if this is just a "gut healing" situation and you only need to do elemental formula for a month or so, that would save you SO much money (not to mention achieving your goal of being able to continue to breastfeed, for all its tangible and intangible benefits!).
Pay attention to the mixing instructions for the Neocate; it's different than other formulas.
And, it's already been said, but obviously the Hypo formulas don't work for all babies; 10% will not be able to tolerate even those "Hypo" formulas - dd1 was one of those kiddos. I suspect that dd2 would have been one of those kiddos too, as she reacted to a body wash whose ingredients changed to include dairy derivatives - something I didn't even ingest!
I still think it's curious that there's no stool sign at all - and think it's a good idea to see about re-screening the newborn tests to see if something turns up there.
I am really hoping that moving to an elemental formula will help while you're continuing to pump and hope to return to nursing. You are narrowing options down, even though I know you really want answers NOW NOW NOW (that's natural) - every time you realize something's not working you are getting closer to finding what WILL work.