The current in the Copper River at Mile 36 is often in the range of 8-10 knots and the channel is at least 300 yards wide. It's a big, mean river and I don't think a packraft is gonna make it across there!
During the past couple of summers, the Cordova-based owner of Orca Adventures Lodge has occasionally been running passengers from the Mile 36 river channel in an approximately 30' aluminum bowpicker converted to a landing craft. He runs several miles upriver to the Million Dollar Bridge area. The price of admission is steep, approaching the neighborhood of the fare for a small plane charter.
Late in the summer of 2009, the tributary less than a mile upriver from the Million Dollar Bridge was essentially dry and I rode across on my TW200. Sometimes it's a dry wash, sometimes a raging torrent. I didn't explore beyond, though, as the alders were very thick. I've been told that a trail was brushed through the alders for several miles since that time. Water flow at any tributary or in the main river channels is highly variable.
I think the strategy for passage along the lower sections of the old railbed would involve a lot of brush removal and many adventures of an amphibious nature. The upper sections would likely include spelunking through tunnels and rock climbing around/over trestle abutments, cliffs and blocked tunnels, in addition to periodic deep (and probably swift) water navigation.
Sounds like the perfect adventure for someone who is thick of wallet, strong of back and weak of mind. Please report back after a few months and tell us how it went!