If you're willing to hang out with rafters, you may be able to find one or two who are willing to carry your beer and gear on the trip. You'll have to get used to eating steaks cooked over a grill or brownies from a Dutch oven, drinking ice-cold beer, and sleeping in a tent with a comfy sleeping pad and bag, hanging out in a camp chair by a nice fire, and general hedonism, though. If you're lucky with your choice of rafters, they'll be the kind that don't mind hanging out at playspots while kayakers surf for awhile. A motor will be a definite plus considering the miles of flatwater on a Cat trip.
That said, I once met a German couple on a float trip. They were doing about 4 or 5 days on the White River and, when I offered to take back the empty can from the beer I'd given him so he wouldn't have extra volume/weight to carry out, he declined and said that they'd once done 9 days self-supporting with those old Prijons.
But seriously, you may be able to hook up with a private raft trip - contact me offline and I'll tell you how to get in touch with rafting groups where you'll have a better chance of doing so.
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse