If you think the Tlingit - really the only Alaska Native people approaching the level of organisation you imagine - would play nice with any government’s harebrained resettlement scheme, I can only suggest looking into Tlingit history. Pre-American Pacific Northwestern culture was extremely violent, honour-bound, and hierarchical; just abolishing outright slavery in the Northwest was a huge job for the British and American colonial governments there. This suggestion is analogous to Britain asking Ugandans to settle Australia for them.
I hate to pull out the “do your own research” card here, because it eliminates the possibility of futher discussion, but I really don’t think you understand enough about Alaskan history to posit a divergence like this if you don’t understand the (absolutely insuperable) challenges to it. Alaska Natives didn’t want to move to Texas, couldn’t move to Texas, shouldn’t have moved to Texas, and wouldn’t have helped anyone - including themselves - if they somehow got there. If you had posted this as its own scenario, I’d have been happy to go into a lot of detail with you about why it’s implausible, and suggest interesting alternative PoDs regarding Alaska Native societies - but since you’ve posted it as a small part of a wider scenario, all I can offer is: it doesn’t make any sense, and unless it’s absolutely essential to your timeline working out the way you want it to, you should ditch the whole idea pending a lot more research into Alaskan history.