At this supposed meeting, if it occurs, ferchrissake take notes.
TFN will have "briefed" the Minister and his staff to the eyeballs, and he isn't going to believe your representatives at all, because he isn't the sharpest knife in the set, and, being a Minister, he has to make decisions on the basis of the advice given to him by his Department, and they are going to tow the AsA line for sure.
In my opinion. your only hope is to repeat over and over again your mantra about staff numbers being critical due to fatigue and excessive overtime, and that even if your pay is doubled, it ain't going to make a difference.
My guess is that you are going to come away empty handed or worse, and that the accident that is inevitably going to occur will claim the Ministers scalp as well.