In my company the MEL is the document on the gate and during pushback. The QRH comes into effect after the aircraft has moved under its own power. To answer some of the above questions:
If something like a bleed valve fails - we check the QRH, it says "if on the ground, do not take off, if in the air press....etc"
The MEL says "one may be locked out etc..", so in this case, even though the MEL has ceased to be the main reference document, the safety of the flight is assured.
If an FMC fails for instance, then there is not much difference between take off and taxiing out, you are still presented with the same problems after rotate.
If you as the commander are not happy - come back to the gate. No matter what happens and which document you consult, if you are not happy, return or land at your discretion.
It works very well for us and hasn't presented any safety issues.
I have gone back to the gate after consulting the MEL after taxy and decided to stay and get it fixed, even though both documents say it is OK to continue. I have also continued with an item that was "no dispatch" in the MEL, but allowable in the QRH.