"we really do have to squeeze everything (and maybe up to a week or more of food) in one pack plus a few subsidiary pouches."
Been there, done that. Not on the scale or scope of your 800-mile journey, but multiple nights with a 2-year-old in the Kelty child carrier on my very obviously pregnant wife. She got lots of comments, "hiking for two?, er, three?" and then they'd look at me and realize that I had be carrying most everything for everyone. Works pretty well in upland Hawaii. Less so in Cook Inlet in March! And you've got four set of clothes, sleeping gear, etc.
Have you considered any kind of a rickshaw? I made one - just as a kid's toy for the driveway - that works quite well, although for trail use, I'd redo it in many way. I started with the two-wheeled cradle for schelping kayaks and canoes. Compact but wide tires, nice bearings, low height. When I've kicked around a similar trip, I also gravitate to thoughts of a decked canoe-like craft, probably stitch-and-glue construction, about 28 pounds, on removable wheels, balanced to take most of the weight, attached to and therefore steered by a waist belt. Get to a bay or stream: remove wheels, toss them in, paddle across, than back to walking.
Also, AND THIS COULD BE A BIG PLUS, consider the tides in Cook Inlet. 4 or 5 knots in some places at times, but even 1-2 knots of current, plus 1-2 knots of paddling and you're going place. 10-15 miles during a single flood up the east side or during an ebb down the west side. Do you imagine doing that in the pack rafts when the tides and winds allow? Your paddling speed would be quite low, it would mostly be in the tidal flow. Throwing sticks in the water every 30 minutes would let you see when the stick was making more progress than the hikers.
And yet, having a rigid craft, speedier and more voluminous though it is, could be very limiting (as you know more than most anyone). You're not going to climb a cliff or scramble through the devil's club with a canoe in tow, whereas you can thrash through anything inland, if for some reason the waterways aren't viable.
Along the lines of psychology - can your four-year-old carry a bit of volume? Does it help to feel like they're contributing? Sea-to-summit's day pack is 2.7 ounces and a sweater, hat and snack would easily fit inside.
Edited to add: Got your PM. I'll email direct about camping, shopping, and contact info for various local industrialists.