AS,
As an ATSA at EGCC who works the DSM (Departure Slot Monitor) and use the phone to Flow, I can assure you that IF you are on stand 212R and EGCC is on either dual Westerlies (24L) or single Easterlies (06L) and you call for start at minus 10mins to slot ALL the team,(all 7 of us)will honestly try to get you on your (as you say) merry way. But if you are number 3 or even higher in call order, that is when ATC get "huffy" at "It's MY 15mins tolerance"
As has been said, come and visit