I had a party of 14 for a New Year's cruise this past December and used Galveston shuttle and limo.
Caveat: We stayed overnight in the Galleria area (have a relative in Sugarland so we met up with her) and got the shuttle from there. Cost was $410 all in prepaid.
We had one of those large vans that comfortably fit everyone and our bags. Driver offered to stop at Buc-ee's or a Wal-Mart for any last minute "I forgots" but we were all set.
With all that said, 7 is a bit of an awkward number for the private shuttles, and you may actually be better off getting a couple of Uber/Lyft to Galveston.