Hi all - first post, help appreciated.

I am using Star Alliance miles from BMI Diamond Club to fund a flight from London to Mexico. It is business class, but I am unclear about what my baggage allowance. The LON to LAX leg is on Air NZ, which allows 3 bags, but the LAX to MEX leg is on United, which I believe only allows 2 bags. I am thinking that I will be checking in to Air New Zealand at Heathrow, and hopefully my bags will automatically be transferred to the United flight while I transit in LA. I will be exceeding my United baggage limit, but I'm hoping noone will notice...

Have I got this right?