Either way, you're going to be flying a period of time on UA without status, since you can't (legitimately) accrue UA miles while your US number is on the ticket.

You might as well suck it up and do it now. Especially if your employer is willing to pay for the E+ upgrade on the Australia trip (entirely reasonable).

The real status benefits for USA-based flyers are E+ seats and occasional upgrades, both of which are only going to happen with regularity if you're using a carrier's own program. (Free baggage and priority boarding are the other key benefits, but getting the UA credit card would take care of those, at least on your personal travel. BTW, did you get the UA credit card yet? There's a thread in the Credit Card Programs section for a total of 55k signup bonus and no annual fee first year.)