If your Girl Scout cookie boxes fit into flat rate priority boxes (5x8x11), then it is $8.10 to mail a box regardless of weight.
Last year a group at Microsoft sponsored sending around 100 boxes of Girl Scout cookies to Stryker Brigade at Mosul. They had them shipped to one of our members on the East Coast where the priority shipping rate is cheapest for large boxes and paid her for the postage (or they tried to, I don't know if she accepted it).
Brad Cloven spearheaded that effort from Microsoft and Mo1 was the one who took them to the post office and did the final mailing.
I'm pinging him along with you for this post. Where is your local guard unit deployed? No doubt they will love getting that many boxes of cookies if you can figure out how to pay for mailing them.
You could also approach your local Rotary or another service organization in your area about covering the mailing costs.
Another thing you can do is charge extra per box to cover your mailing costs.
Good luck!