I think I may have a suggestion. I can set the mmgt to midi clock off (midi settings). Setup menu has "calculate flashes ON (the axe doesnt really sync nor send a midi clock like the norm/standard. Total pain in the ass and fractals fault). Show tempo is ON (if you want it to show it on big screen momentarily). THEN create a button on the mmgt for tempo. The button is a standard IA button set to no group, no cc link, remote ctl off, ia link off, snd on preset off, update on pre off, tempo ON, show tempo ON, momentary OFF, on msg only OFF. The button has one action and mine is type 'cc momentary", device axe fx, cc14, off value NONE, on value 127. The axe is set up to send realtime sysex all ( i like my tuner). I dont think having a preset tempo for the mmgt preset would make a difference, since the tempo for the mmgt is set to off. But I dont recall, so perhaps leaving the preset tempo empty would be the best bet. From your desription, it sounds like you just need to turn "calculate temp" on. Remember, the axe send messages in a timely manner for tempo, rather than an actual clock number...i think.
This is the closest I can get to 'locking' tempo with an axe unit. It is a recent update to the mmgt to calculate flashes, and its pretty damn close. The issue you are describing, is something that has been a loong road to overcome. I really do give credit to Ron and blame Cliff, but both the axe and mmgt are great units, tho querky. Just wait until you try and toss a daw into the clock mix, then it gets really challenging.
Best of luck, i am a novice myself on the mmgt, so i hope this helps, wont be surprised if it doesnt.