An interesting thread!
FWIW, I believe that the OP has a very limited chance of clearing the upgrade as 1P with any upgrade instrument since LAX-IAD is a route that is heavily travelled by 1K members. This would be especially true on flights with the AB320. Flights on the 757 are a crap shoot at best.
But, hope can spring eternal

There are 2 flights with large aircrafts, a 777 and a 767, and perhaps 1P may have a good chance on those flights?