If other solutions don't work you could try modifying the driver to install for both types -
> unzip the Quadro whql.exe with 7zip and modify the nv_dispwi.inf (in Display.Driver) listings to include the GeForce card- there are a few places to do that - and install and it should recognise both. I have done this for years for Win 7 - not sure if it is exactly the same for Win 10 but it will be similar.
It would be better to pick a Quadro driver where there is also a Geforce driver with the same reference number - that is there is a Quadro driver abc.xyz for the 5000 and a Geforce driver abc.xyz for the 1080
Try a search of 'Nvidia INF driver modding' to get help on how to do this. You may find a recent .inf on guru3d forums although those usually are changed to list all cards which is probably unnecessary.
Hope that helps. Sorry I'm too busy to assist further other than to point you in the direction of a solution