SOLVED PROBLEM
Run the trainer as admin AND in compatibility mode for Windows 7. Then, when you hit one of those objectives, save your game and reload it. Don't bother relaunching. Saving and reloading will bring the health bars to their proper state, though units that pick up a damage texture will keep it once repaired, so your entire force may in some cases look like it's fresh out of Hell.

[Edited by Apache49, 3/9/2015 10:00:58 PM]