The Parks Highway goes from Wasilla north to Denali to Fairbanks.
The Glenn Highway goes from Anchorage east to Glennallen (intersects the Richardson Highway, which goes north and south, toward Valdez and Fairbanks).
The Denali Highway goes from Cantwell (south of Denali NP entrance) to Paxson (which is on the Richardson Highway).
I was suggesting Denali NP south on the Parks Highway, then east on the Glenn Highway to avoid the Denali Highway if your car rental company prohibits it.
You can certainly drive on roads prohibited by the rental car company. But then you are liable for 100% of the damage, even if you accepted their coverages and waivers. Also, most third party coverages (credit card, travel insurance, personal auto insurance) don't cover you if you violate the rental contract.
If you drive either the Denali Highway or the McCarthy Road, it will make the car absolutely filthy. Inside and out, doorjams, you name it. If you don't spend close to an hour cleaning the car and running it through a car wash, there is no way in the world you can hide that you drove on such roads.
Thanks a lot for clarifying - I have always been confused about the exact location of the Denali Highway and this clears it up. I would like to avoid driving on those roads as well (to the extent the agreement prohibits it) and this would be a nice workaround.
Thanks again for the help - I will post updates to the itinerary once it is finalized in case it is helpful to others as well.