I agree that it would be in your daughter's best interest to go to an earlier orientation session if at all possible. UT recruitment is brutal in the best of circumstances. I know last year there were some conflicts with the girls that were on cheer and pom squad, as well as late orientation girls. Each of the sororities sent representatives to meet with them. There is a good chance that they will do the same this year...however, I don't know how sucessful those girls were in the process. The greeklife office really does try to work to make sure every girl has a chance, but they can only do so much.
As far as the May deadline...this was crucial back in the day when it was legal to "pre-rush" at orientation. The chapters wanted to get packets before the first orietation session in June, so that they could contact girls and arrange to meet them during orientation. This is no longer "legal"..not saying it doesn't happen..but those chapters that are caught, get heafty fines. If I had a daughter going through recruitment at UT and she was contacted by a sorority for orientation, I would tell her to politley decline the invitation.

I would however encourage her make as many contacts as possible while there and to conduct herself in a positive light at all times. She will be watched.
That being said, the earlier the better..each chapter gets hundreds if not thousands of packets throughout the summer and I would guess that after a while they all start blending together.
Good luck to your daughter!