Thanks for all your comments. I appreciate your opinions on this subject. I do still believe that this creative ticket would work just fine, because:

1. AS and UA are competitors and would not likely exchange "no-show" information in real time
2. The rules of F class fares allow for an unlimited number of stopovers. Therefore, the traveler could schedule a LAX stopover of a week, for instance, then call UA to confirm the LAX-LHR flight a day before departure.
3. The traveler could easily schedule a stopover in LHR, as allowed by the fare.
4. If UA gives the traveler any trouble, the traveler can always get the ticket refunded.

This creative ticket would have its best chance of success when the airlines are not in a common alliance and, in fact, are competitors in their respective markets.

Anyone want to spot me $3K, and I'll give a go!