If you're desperate for her back it is possible, and without taking very long. I lost Genji a couple of months ago and recently got him back, I managed to complete the 16 villager cycle in about 3 days, just cycling between two two villagers (9th and 10th). That's if you want to of course, it is pretty frustrating but I managed to do it without losing anybody else. Really wanted him back so I was willing to do anything really....
It's a massive pain that we can't stop villagers moving after finding them in boxes. Things were simpler in wild world
all of my villagers were suppose to be permanent! 
how long do you have to wait to get the same villager back?
