That is a huge improvement and one that will lead to having a memorable trip for all the right reasons. It will be at least 10-15% more in mileage by the time you add in detours to the parks and driving around in them, but even then your trip can remain quite relaxed while keeping on the move. I would probably look at taking 4 days to get out to the Badlands and 5 to get home from Jackson which will give time for short breaks away from the car, or an early evening off the road to spend in town. That would be around 3800 miles 'taken care of', leaving you 12 days to sight see in the west while covering around 1800 miles with detours. At least 3 of those days I would plan on spending in, or around Yellowstone and the Tetons.
Ultimately only you can decide if it's too much as everyone is different, but it's certainly possible while having time to enjoy sights along the way imo.