I am not familiar with AP rules with *A awards, but from what it is on UA, I can give you following advice:

1) UA F is nothing special so try to find SQ or NH F for your flights to Asia. But if UA F is the only thing you can find, it still is a F product and it will be nicer than most of C flights.

2) SQ has F class routes from SFO (to HKG or ICN and to SIN) and LAX (NRT to SIN) (and JFK to FRA to SIN - this goes via Europe and I am not sure this is possible with AP miles). NH can be had on flights from ORD, IAD, JFK, SFO, and LAX. JFK and IAD route may cause some problems of "back tracking."

3) There is also OZ (Asiana) F you can certainly try. The seats are older than UA F, but the level of service provided is very very good, at SQ level. OZ flies F product from LAX, ORD, and JFK to ICN.

4) So, you have four *A airline choices for your F trip to Asia from N.America. With UA awards, there is maximum permitted mileage that may get in the way of "scoring" certain routings, but you can always try to see if you can connect in SIN to BKK.

5) To summarize, your US gateway to F class product is as follows:
LAX, IAD, JFK, SFO, and ORD
Your Asian gateway to F class prodcut to SIN or BKK is as follows:
ICN, NRT, HKG

Good luck!