Wow, your trip ends right on the cusp of a wonderful opportunity....
Each year Denali Park offers a road lottery for winners to drive their own cars into the park (all the way to Wonder Lake). I consider this the BEST time to go to Denali Park. You can avoid the long, tourist filled bus ride and drive your own vehicle at your leisure. The dates this year are going to be Sept 14 - 17th. If you can tour the park on the 14th and still make your flight on the 15th (if it's a redeye), that's they way I'd want to go.
For more information, check here:
One other note about the road lottery; on these dates Sept 14th - 17th there are no longer ANY shuttle buses transporting tourists up the mountain. So make sure that your plan to take the bus to Wonder Lake is not over one of these dates.
Lastly, if you apply for the lottery ($10 per person) and don't win, you can usually buy one off craigslist. If you win, but don't get your preferred date of travel, people also trade road passes by listing on craigslist.
Good luck and enjoy Alaska!