You’ve certainly got your work cut out for you over the tundra and tussocks traveling with a paraplegic, but if you plan correctly, and take a few safety precautions and are willing to accept if things don’t go the way you planned in the Brooks Range, than who I am to dissuade you from trying.
I’ve hiked from Anaktuvuk and packrafted the Alatna, but did a slightly different route than what you are planning. I and a friend floated out of Anaktuvuk via the John, to the Eyokpuk river and hiked up that over the continental divide to Agiak Lake. Floated part of the Agiak River to near lonely lake and then slogged through tussocks to Easter Creek floating from there to the Killik. Hiked up the Killik and over to the Alatna and then floated down the Alatna until portaging over to the Tobuk River and floating into Iniakuk Lake Lodge. A little more than 11 days total.
I am also a part time guide now in that area, some in the summer but mostly in the winter doing dog mushing and would suggest that you contact Brooks Range aviation (email@example.com) or possibly Bettles Air Service to set up your food drop at Circle Lake or Takahula. Takahula Lake is probably easier to locate while floating along the river and to get to than Circle Lake. Brooks Range Aviation likes to land on the south edge of Takahula Lake, so you would have to hike the mile or so over from the Alatna to Takahula and then inflate your packraft and paddle across the lake and get your supplies to bring them back to that Alatna. The Alatna also flattens out and slows down considerably after Takahula, so you might want to consider getting picked up there instead of just the food drop. I do understand it is cheaper to fly Wrights Air Service into Anaktuvuk and then out of Allakaket instead of a bush plane pick-up but they don’t jokingly call it the aFLATna for nothing. If the wind is blowing strong, you might be better off sleeping during the day and paddling at night when the wind dies down.
The outfit I work for, Iniakuk Lake Lodge has a cabin at the headwaters of the Alatna, and one also at the confluence of the Nahtuk and the Alatna. They don’t allow people to stay there without a guide since their business relies on the condition and care of their facilities, but if you were inclined to look into staying there, their website is www.gofarnorth.com. Either I or the owner (Pat’s son) John will be out there with some clients in later August as well, so we might see you on the river regardless.
Since I do dog mush guiding in the winter I have only been up the Nahtuk River in the winter, but there is a canyon (beautiful ice falls in the winter) a few miles up the river from it’s confluence with the Alatna, and it is pretty narrow. Pat’s son John might be able to give you some more information about what the river looks like in the summer since he has done more hiking around there than I have, but I know he hasn’t packrafted it, since we’ve both discussed whether it would be possible.
If you have any other questions since I wasn’t able to answer all of yours let me know. Otherwise, the Park Ranger in Anaktuvuk Pass was Al Smith when I was through there and he was pretty helpful (firstname.lastname@example.org).