Ok this is weird... I rarely use live view, actuall I never use live view. I performed a quick test, far from ideal conditions, right here on my desk shooting at a book. I noticed that the if I use live-view and Autofocus, it works ok (after 10 shots focus is spot on). But if I shoot at the same spot, without live view I'm back to square one with the camera focusing aprox 1 cm to close. I know that live view uses contrast detection and normal shooting uses phase detection, could my problem be with the phase detection system? It's sensors or something like that?
If the focusing ground glass is out of adjustment, how hard is it to fix? I mean, is it routine or mayor surgery? (Assuming that all it needs is an adjustment).
It could be an indication that you need to put in corrections in the focus fine adjustment for that lens. If the focus with live view is OK and the other is not, then corrections should fix it.
The focusing screen correction would be used if when the focus is acquired it would not be in focus in the viewfinder.
But from your description of the situation you are facing, I think that the focus adjustment of the camera can be made. Try this, focus using the auto-focus or the range finder lights. After the focus is acquired, turn the auto focus OFF. then turn on LiveView to see where the focus actually is using the magnifier. Then make a fine focus adjustment and test again. Oh, I forgot to mention that all this HAS to be done on a sturdy tripod.
After finding the right focus adjustment, make certain to save it for that lens.
Keep us informed.