I know the subject line seems to be a presumed impossibility, but I just wanted to share that these awards do exist. Additionally, they can be incorporated into the biggest sweet spot I've found in United's award chart. I have only seen these awards on the Auckland route, so that's where I did more depth searching.
Caveat to all of this? You may need to call United to make the booking and you'll need an agent who doesn't give up. It's absolutely possible to get one of these seats, I did, but I had to listen to quite a few agents tell me that they couldn't do it before I found one who could.

SIN-AKL
04 Mar
07 Mar
20 Mar
29 Oct
30 Oct
31 Oct
03 Nov
04 Nov
05 Nov
06 Nov
10 Nov
11 Nov
12 Nov
13 Nov
17 Nov
18 Nov
20 Nov
21 Nov
24 Nov
25 Nov
26 Nov
01 Dec
02 Dec
03 Dec

AKL-SIN​​​​​​
05 Feb
28 Oct
29 Oct
30 Oct
31 Oct
03 Nov
04 Nov
05 Nov
06 Nov
07 Nov
10 Nov
11 Nov
12 Nov
13 Nov
14 Nov
18 Nov
19 Nov
20 Nov
24 Nov
25 Nov
26 Nov
27 Nov
28 Nov
01 Dec
02 Dec
03 Dec

So what's the sweet spot? Oceania to Australia/New Zealand. Oceania is pretty much every island in the Pacific smaller than Hawaii, but if you look at where Star Alliance airlines operate, it's essentially United's Island Hopper, which means Guam. Sure, it's also PPT and the rest of the South Pacific, but there are no flights between PPT and GUM that cost 12,500 miles. It's essentially a separate region within the Oceania region.

In terms of getting from AUK to GUM you will obviously transfer in SIN if you're in Suites. If you stop there (South Asia as defined by the award chart), you're paying 65,000 miles for your F seat.
But if you go to Guam, you will fly up to 7 more hours in F or J to either Japan (various cities), Hong Kong, or Manila before hopping on United metal to Guam and you end up paying only 60,000 miles.

Not bad, huh?