To help your chances, you should also post some info about your river running experience, what group gear you can provide and so forth. Also if you post on the Grand Canyon Private Boaters email list that'll get you in contact with others planning their trips that may have an opening.
I just did a search on "Grand Canyon" and found this post of a July 28 trip looking for boaters
that may be just what you're looking for.
Good luck finding a trip!
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