OP, did you look for plain MIA-MLE (rather than assuming you'd need to get to a gateway like JFK/LAX)? I know you already have something you like for that leg on hold, but there are (IMO) better options than what you have. Like:

11/15: MIA-ZRH-IST-MLE on Swiss/Turkish, business, 80k UA
12/7: MIA-IST-MLE on Turkish, business, 80k UA
11/16: MIA-IST-MLE on Turkish, business/economy, 80k UA (hope business opens up for IST-MLE later)

If you're interested in a day in Abu Dhabi, there's pretty solid availability on Etihad for MLE-AUH in Y connecting to AUH-MEL in F or AUH-SYD in J (on the A380). Unfortunately that's a route that just went up from 45k/60k to 80k/100k for J/F. EY only has 1 flight per day MLE-AUH and it arrives at 10:55pm, so you'd have to (/get to) overnight in Abu Dhabi. One of the AUH-SYD flights (the A380) leaves at 10:05pm, perfect if you want to spend a day in AUH.

As for getting home, that's going to be tough undoubtedly. High season premium class Australia-US. If you're comfortable with the risk, you may want to book the rest and cross your fingers. Air NZ has been releasing business class seats about 3 months out lately, so you could get lucky with that (they fly to LAX, SFO, and IAH from AKL).