"And I made every deal I could think of, to any god that would listen..."
"And did it work?"
"...not exactly."
A lot of folks have speculated the "god" that listened was the Monitor, and one of the people in the unit who died was John Diggle.
Had this scene never existed, your theory would be viable. But, since it does, it would be kinda odd that they brought this up THIS SEASON, then instead reach back several seasons to the gender switch via Barry's time shenanigans as the ACTUAL reason to explain her allegiance to Monitor.