The past two Septembers upon returning home to Interior Alaska from Jasper took me 6 days of travel which was practically a direct route, as compared to commuting southbound along different routes or sidetrips would be a venture of 9 to 12 days for me before reaching Banff and Jasper areas in my old camper rig that I will not abuse or tear up.
Since I only was authorized three weeks vacation the last two Septembers and always behind schedule 2 or 3 days before heading back home northbound, I had only 7 days left before returning to work as I made it back home on time the night before both times.
The 6 days from Jasper to home was pushing it for me although it was roughly 300 miles per day, but that was also dealing with road construction zones, stretches of frost heaved roads in between as I drive between 5mph to 25mph thru those rough intermittent stretches, driving by covering more ground during nightfall as well which I don't care for, as it gets much darker during mid August and September.
In between despite the construction zones and road surfaces in some parts of the Alaska Highway, you have potential pilot escorts to deal with as in Central BC there are a lot of gas well equipment being hauled around by semis as they are gearing up for winter too, as well as in a hurry southbound traffic racing to get away from Alaska as they think wintertime will be the end of the world for them and god knows how fast they driven across the bad surfaces with their trailers in tow, and the colder it gets with snowcapped mountains in those areas you have a potential increase of wildlife roaming around to get away from the hills as these other factors could or would slow a driver down as this is why I do not change my driving habits or speed and pay closer attention to other drivers and road surfaces, I am rather driving much longer to gain ground which all depends on how many times I need to slow down for any of these other factors I mentioned along the way.
Upon leaving Parks Canada from Jasper returning home, in 2011 and 2012 was where my layover spots were :
Day 1 - Jasper to Dawson Creek BC - Grande Prairie AB
Day 2 - Dawson Creek BC or Grande Prairie AB to Fort Nelson BC
Day 3 - Fort Nelson BC to Watson Lake YT - Rancheria YT
Day 4 - Watson Lake YT or Rancheria YT to Sue's place between Whitehorse YT and Haines Junction YT
Day 5 - Sue's place to White River YT (55 miles from the Alaska Border) -260 mile stretch here-
Day 6 - White River YT to home which is 330 miles.
Between Destruction Bay and the Alaska Border is a 140 mile stretch of intermittent frost heave road that is pretty bumpy as this stretch can break components of a vehicle and or trailer should a driver want to make time on, there are a few spots between Whitehorse and Haines Junction that have hardcore bumps too so slow down in these bumpy areas if you want to commute damage free.
Just a note upon driving my rig between Destruction Bay and White River is an 80 mile stretch and takes me between 3:30 and 3:50 to drive thru this stretch and that is non stop driving averaging 20 to 23mph in my old camper rig.
Upon this analysis you can reach Denali Nat'l Park in 7 days from Jasper Nat'l Park upon a 300 mile per day stretch on average while driving "safewise" with all the elements in between, while still enjoying one to three hours per day of stops while on the road prior to overnighting.....If you want to take on the more sights in between during the day, then I would say 300 miles per day is not doable by any means.
I would not worry about making reservations for Denali unless it was Labor Day Weekend, and as suggested you could also opt to make a reservation within one day or two from Denali once you are in Alaska.
If for some reason the Denali campgrounds of choice are full upon your arrival, there are other RV places to camp at that are nearby the National Park so no sweating it there either.
Depending on how many road construction projects and repairs are going on, you can make cruising time upon 85% to 90% of the Alaska Highway which is pretty good road surface.
Hope this perspective helps.