It has given me a lot of grief over the last few years with this. Some times it just wouldn’t work, no matter what I tried and eventually I’d do something that somehow fixed it and could never remember for the next time. It was really quite annoying and frustrating.
After every windows update, it would happen again because windows would overwrite the drivers I’d manually install and the changes I’d made and screw it up again.
My G27 died a while back and for a replacement, I decided to stay away from the Logitech wheels (even though they are quite good), simply because of all the driver issues.
I went with the Thrustmaster TMX this time and paired it with the G27 pedals & shifter using the stand-alone shifter adapter you linked to and another adapter that let’s you use the G27 pedals with the TMX/T150 wheel.
Haven’t had a single issue thus far with the new wheel. It’s really surprising though, that these issues haven’t been properly fixed on windows or logitech’s side, knowing how wide-spread the problems is.