For FAI to beat UAI, sufficient work on FAI needs to be done before sufficient work on AI is done.

If slowing the world economy doesn't change the proportion of work done on things, then a slower world economy doesn't increase the chance of FAI over UAI, it merely delays the time at which one or the other happens. Without specifying how the worlds production is turned down, wouldn't we need to assume that EY's productivity is turned down along with the rest of the world's?

If we assume all of humanity except EY slows down, AND that EY is turning the FAI knob harder than the other knobs relative to the rest of humanity, then we increase the chance of FAI preceding UAI.