It is better that you have the recs you got than no recs at all.
Fake nails are OK as long as they don't look fake. I'm sure there's some nail-biters and weak-nailed sisters in the sororities who'll be sporting them too.
I personally would skip the strapless dresses since your other options for those parties are great and so you have one less thing (is my dress staying up?) to worry about.