At my airline, during the period you describe ( between push back and takeoff) , the QRH is the 'operational document' and must be actioned, while the MEL is now a 'reference document' that must be consulted but not necessarily actioned.
What that means in reality is that after running the QRH, the Captain is required to pull out the DDG and read the applicable MEL, he or she can then make their own call on whether to return to blocks, carry on, or carry on after implementing any (O) items that they feel would benefit.
There is no requirement to return to blocks if the MEL contains an (M) item or anything else, the discretion is completely with the PIC , keeping in mind that the PIC must read the MEL.
That's how it works at my joint.
Cheers