I see you hail from South Carolina. As a suggestion? Do your planning with wriggle room. If the Parkway happens to be socked in with weather when you get to Calgary, look at heading to BC and then north via 93 from just west of Banff then head north on the 95, picking up the #1 again just north of Valemont and think of hitting the Parkway on your way home.
A trip of this magnitude..the trick..the secret, is to not be wedded to your hoped for travel routing. Be flexible. 100% bendy bendy, so that when the need arises no one gets bent out of joint. Look for the other way and carry on. Chances are, that will happen more often than you thought was gonna. You'll get to Alaska and have a great time doing it.
Gary Haupt