First, you don't need a reservation for Denali at this time of year. We easily got a site in Riley Creek campground without a reservation although we pulled into Denali early morning. By 1:00 the campground was full - but this was in July. You'll find that most folks are leaving Alaska at this time so there will be plenty of room for you.
If you feel better about having a reservation just wait until you can better judge your timing and call about 2 days before arrival. You'll have no problem.
As far as driving many miles a day and staying on a schedule, we wouldn't recommend it. This is probably your first trip to Alaska and there is just so much to see along the way. Why pass them up? Are you going to return multiple times? Also, you can't count on the roads being in excellent condition because they won't be. If you try flying on them at 55-65mph you're going to break something. The key is to travel slow.
Hope you have an enjoyable, 'relaxing' drive to Denali!!!