MCT is 3 hours for NZ->UA at LAX!

As long as you can use the american line at immigration you should make a 2 hour connection, provided the NZ flight isn't late. If you use the alien line then 2 hours is a risky connection for NZ->anything (but okay in the other direction domestic->NZ).

I normally err on having a longer connection and if I get through airside T6/7/8 early enough waitlist for the earlier flight.

You will not be able to check in across separate tickets, although bags can be tagged to your final destination (you'll still need to pick them up at LAX to take through customs for MEL-AKL-LAX-DEN).