First message indicates MR is ex-WAS, but home airport is LAX...is it WAS you are requesting? Also, is 1K still correct? (I think GS upgrades into PN)
As desirable as an international with the minimum number of flights, it's really hard to find something affordable with space. If you're seeing 10cpm for W-fare with >R0, that's really hard to justify. Premier Accelerator at 11cpm seems real attractive at that point.
Another option is try something domestic/Carribbean. Here's an option...combine these two:
WAS-BQN(Econ):
http://goo.gl/flights/BbNd
BQN-HNL(First):
http://goo.gl/flights/DvAs
So it would look like this:
Fri 22 Jan
UA4269 DCA-CLE 1430-1555 E45 (L single cabin)
UA1138 CLE-EWR 1707-1851 73G (L)
UA1071 EWR-BQN 2114-0159(+1) 739 (L)
Sat 23 Jan
UA1162 BQN-EWR 0255-0555 739 (P/First)
UA15 EWR-HNL 0910-1533 764 (P/First lay-flat)
UA1229 HNL-LAX 2330-0659(+1) 753 (P/First)
UA1549 LAX-IAH 0829-1350 739 (P/First)
UA1945 IAH-EWR 1427-1855 739 (P/First)
UA1071 EWR-BQN 2114-0159(+1) (P/First)
Sun 24 Jan
UA1169 BQN-EWR 0255-0555 739 (L)
UA4646 EWR-DCA 0904-1025 E45 (L single-cabin)
WAS-BQN L-fare $309 4670PQM
BQN-HNL P-fare $1316 26934PQM
TOTAL $1624 31604PQM 5.13cpm
Seems like a waste to use a GPU as an RPU for the WAS-BQN segments, but better than letting them rot. And the 11h23m EWR-HNL is lay-flat. I haven't checked availability, but typically EWR-BQN is super easy.
Good luck!