The less troublesome deal may be Canada-Singapore round trip for $611 (google search; slightly higher on united.com). After about Oct. 28 when UA starts twice-daily SFO-SIN flights, you can have 14 hours on ground (arriving at 8:00 am and leaving at 10:00 pm). You can search YUL/YYZ/YOW-LAX, LAX-SIN, SIN-IAD, IAD-YUL/YYZ/YOW. For example, if you depart from YUL, you can get YUL-IAD-LAX-SFO-SIN-SFO-EWR-IAD-YUL to maximize your PQM. The cpm is about 2.6 with 500 min miles. Here is an example:
https://www.google.com/flights#flt=Y...024*.USD.61024