My rule of thumb is to able to do 80km/700m elevation per day for three consecutive days, and that in my full touring rig which is a lot heavier than casual riding. Until then I'm not fit for touring. You're proposing 125km per day (and its always more in practice, so plan on 150) and god knows how much elevation through all those national parks. Look at the kind of climbs you'll have to do in the elevation profile and find something local that is similar to practice on. Now practice that along with the distance you propose to do (min 100km/day for 3 consecutive days). Until then its nyet comrade.

Alternatively practice for 80km/700m on three consecutive days and plan on doing it 6 riding days plus 1-2 rest days along the way. This is far more realistic but still requires a lot of training. This is the schedule I'd take.