Seeing as the aircraft is dispatched and the QRH is now the reference book to use
Different (dispatch) horses for different (dispatch) courses. I can only presume that this "dispatch" is applicable in the OPs company (or maybe under FAA regulations generally as the OP's location is Florida). Either way I cannot comment.
FWIW the last three 737 operators that I have flown for, the MMEL/MEL/DDG applied from; a) pushback, b) when the aircraft moved under it's own power, c) to the application of take-off thrust, respectively.
Widening the pattern out a bit: just because the aeroplane has "dispatched" doesn't preclude the use of other applicable checklists/memory items. (If we take the OPs definition of dispatch, we wouldn't be applying an MEL/DDG if we had an engine or APU fire as we taxiied out!). As ever common sense should prevail.