You know to try the factory issue recovery media first. Finding just the right set of drivers and apps to fix this is as you found out almost impossible. I can't tell you since I don't own any model with the 7970 and you omitted make/model number too.
Here, not one laptop in the past 6 years had me selecting which video card to use. There was a lot of progress in the drivers and apps so this issue faded. Except it seems for folk that change OSes.
My friend has a problem with his laptop and I'm trying to solve it for him but nothing seems to work. The problem is as follows: He got an old laptop for cheap and the previous owner replaced the graphics card from an Nvidia one (I don't recall which one) to an AMD 7970 and also switched from windows 7 to windows 10, but his laptop has Intel Integrated graphics which is preventing him from playing most games due to the fact that said games won't choose the right graphics card.
Now this is where the problem gets worse, I tried reinstalling the drivers but the computer freezes, and when I finally install them it says an error occurred and that I should contact AMD so I restore the system to a previous point and let it be. Then I also tried using AMD Crimson to change the graphics card that certain games use but to no avail since the software doesn't even open now... I also tried messing around with the Intel options and the AMD Crimson options back when it used to work but it was no use. So from my research all I'm left with is disabling it on the BIOS settings but I wanted to know if there was a different way to fix this...