I thought maybe the folks involved in this trip might have posted something about how they did the logistics, but I guess not.
As it happens, a contact in the Park Service at GC dropped me a note and explained how they worked this out between the River Office and Backcountry Office regarding permits. It's not a common request, but they evidently are trying to be flexible in working with folks on even unconventional means of access to the river portion of GCNP.
The subject of packrafting didn't come up when setting up the new management plan, but did surface soon after the new CRMP was developed. So far, three different lottery winners have asked the Park to allow them to use their permit as part of a packraft trip. That was allowed with conditions. All packraft trips get a lot of pre-trip-planning input and face-to-face inspection from Rangers prior to their launch. They are allowed to use Wag bags and a somewhat smaller firepan, have to pack out waste, trash, and ashes, and do all the other usual stuff. They check in at Lees Ferry on the original launch date, and then use the river only on the days and places where a normal raft trip would have been had it continued from that launch date.
The Park has also had a few packraft requests for short, mostly backpacking trips, where the packrafts are used mainly to cross the river or get to get to the next backpacking area. Those were authorized solely through a Backcountry Permit.
It seems they would rather engage folks interested in packraft trips rather than have them try and do it without a permit. So far, the report is that everyone doing this has been good at working with the Park staff and seemed to genuinely follow all rules.