Most people would just cough up the miles and fly F both ways . . .

There is no search that allows you to specify F one-way and Y the other at this time. You would have to search for F both ways and see what is available on the outbound (ignoring the return since you don't want F on it), then search for Y both ways and see what is available on the return (ignoring the outbound since you don't want Y on it). After you determine what is available, you would have to pick up the phone and call to do the booking, since you can't split the two awards during the online booking process (unless, as it did in your first case, it just happens to offer you that as the overall lowest option).