but it gets really messy towards the end (I think 7th set?) where we have landmines and a second defensive tower go off before I have everyone topped off

Perhaps reevaluate how you trigger the towers? I understand there's multiple ways to handle the towers as well as when to push phase etc, but if you're solo healing, probably find the best method that has 0 AF threat (You no need to stoneskin/adlo the AF victim), and your above mentioned landmines + defensive tower combo.

I'll list out what my static does that gives us the above conditions:
Wave 5(? I'm not sure which exact wave, but it's the 1 with mines and defensive tower), 2 on Mines, after clearing mines and during second brainjack, push boss below 45% (10 second window, with an extra dps, you probably need to hold dps and wait for the 2nd brainjack, if you can't meet this requirement, sorry can't help you further ), if you did it correctly, Avatar will straight away cast AF, instead of Ballistic Missile.

Wave 6 (starting of 3 tower phases), 2 person on Defensive tower A, 1 person on Defensive Tower B, once the 1st AF blows up, tank enters defensive tower A to manual trigger (5 sec window b4 next AF is applied).

Wave 7, 2 person on Defensive tower, 1 person on mines.