MIAT also has flights out of NRT as well. I've done PEK - ULN and ULN - NRT before. PEK - ULN was on time no issues. ULN - NRT had a small delay as it was unseasonably cold that day and the aircraft had to be deiced. If coming from Chicago, United also sells connections on MIAT on one ticket so a UA / MIAT combo is also a possibility. I also think OZ is getting into ULN as well but I forget when those flights will start.

KE and TK will have a slightly better product. The MIAT planes have a pretty dated interior and the seats are quite cramped. Other than the service was actually pretty good. Flight attendants speak good English and were quite friendly.

A day early is a good idea. Delays aside, I would recommend taking the day anyways just to rest from the long travel and enjoy having regular facilities. Venturing outside of UB is the best part of Mongolia but tourist and bathroom facilities are seriously lacking once you leave UB. You'll be thankful for the one day in the city with a real toilet.