Did a quick route check and from my house to Prince Rupert, BC is 3,271 miles so assuming ~ 500 miles per day that's 6 1/2 days (round off to 7). Then an overnight from Prince Rupert to Haines, AK on a ferry up the inside passage so another couple of days bringing to total to 9. It's 775 miles from Haines to Anchorage so add another couple of days and we arrive in Anchorage 11 days after we leave home. On the way home I would take a different route that skips the ferry up the inside passage. The route I chose is not interstate and puts me in the mountains as soon as possible and keeps me in the mountains as long as possible. There is a more direct route. I have a buddy that rode the Hoka Hey challenge a few years back when the route was from Key West, FL to Homer, AK and he made the run in 8 1/2 days so I'm sure I could make it from Anchorage to Houston in less than 7.
I would say that this round trip could be done in three weeks easily with lots of time for goofing off or a direct ride there and back in 10 days or so.