Folks, thanks for all the helpful suggestions.
ReneeMoss: I did think about opening an E-trade account, but thought there might be too long of a time lag between when you open the account and when the miles are credited. Do you know how long it takes E-trade to credit MileagePlus miles once you open the account?
Matt Wald: Excellent suggestion about transferring miles into/from a hotel program. I looked into the details of the transfer AmEx->HHonors->UA but found that I could only yield 16,000 Mileage Plus miles from 64K AmEx membership miles. But then it occurred to me that I could use my points in Marriott Rewards to get the miles I need on UA, which I had not thought about until I read your suggestion. I think I have enough points in Marriott to get me to the total I need on UA.
I'll try to book the other award on Qantas with my CO miles.
Has anyone here exchanged Marriott points for UA mileage? Just wondering how long it takes for the miles to show up in my Mileage Plus account from the time I initiate the transfer.