I sympathize with your circumstance. It can be tough waiting and not being able to control the timing of your journey.
BUT one could also say beware the Alaska Highway. It closed to all traffic for 4 days in June 2012 due to a bridge washout. Crews worked hard to get traffic flowing again, and it was one way for a long period. The Campbell & Cassiar Highways were closed at the same time so there was no alternative to drive north or southbound. Grocery stores ran low on supplies and some gas stations ran dry.
Beware the Cassiar Highway as well. Extended closures are also common there, usually due to flooding. Forest fires have also closed this route for lengthy periods. Last year the Campbell Highway in Yukon closed due to forest fire, for days.
Thus, it is best to be ready to adapt to any circumstance. Advance reservations can be missed if something happens.
You'll still be able to visit Denali. A few days notice is often all that is needed unless it is a long weekend. If you phone, they might give you special consideration. Commercial enterprises in the north know that stuff happens and often provide exceptions to those affected.