Hi Josh,
Thanks for writing in and apologies for the delay in response. The median GMAT score for Rice is 680, and a 620 has you just inside the middle 80% range. If you think your practice tests are indicative of your potential score, I would suggest going ahead and giving the GMATs another try.
Best of luck!
Daniel Richards
http://www.mbamission.com Read the 
mbaMission Insider's Guides (14 individual school titles)
Visit the 
mbaMission BlogFollow mbaMission on 
Twitter