I went to the NYC consulate yesterday and was granted Indefinite Leave to Enter! yay!
If it hadn't been for this forum I never would have even known that the ILE visa is being discontinued on April 2nd. A HUGE thank-you to everyone here who provided information and advice on this. It's such a relief to know that it's sorted now and I won't have to go through the process (not to mention cost) of applying for ILR in 2 years' time.
For anyone who is going to apply for ILE next week:
In addition to the core documents (application, passports, marriage license) the immigration officer only asked to see 1) bank statments/evidence of savings, 2) evidence of accomodation in the UK, and 3) job references/information on job prospects/CVs (neither one of us has an actual job offer yet; we're not moving until September). He didn't even look at the huge binder of evidence we had gathered of our 4-year marriage/cohabitation. He was very nice and polite, and the whole appointment was over with in less than 15 minutes. I came back to the consulate an hour later to collect my passport, which now has a big shiny ILE visa in it