Alright, solved it. There are a couple of small little bits you can polish if you care to.
>pics 1 and 2
So first thing I noticed, its left shoulder has vertices wildly out of place. That looks to me like they weren't normalized, and when I clicked Normalize All, it changed weight, so yeah that was the issue.
It became pics 3 and 4, it ended up looking a bit wobbly when animated, if you don't like that then experiment with painting it to be the same as the right shoulder (not the same exact keys, but the left-side equivalents. The medic .blend file has them all named which makes it easier)
I assume that's what you mean with the teeth, how there some green and black moving around there during animation. I realized when looking in-game close up that the green was a reflection map (the green was stadium grass. the reflections just use a pre-made texture, not the actual environment, and the .mtl file specifies Basic_CNSR shader (Constant, Normal, Specular, either roughness or reflection not sure which) instead of , for example, Basic_CNS or Pony, so it just used the default reflection map as none was specified)
That's not necessarily a bad thing,just useful to know for other issues. Have a look close up and see what I mean. I've changed the one in my re-upload to Basic_C only, since we don't have/want a normal map or a specular map. I also removed double-sided and alpha as we shouldn't need them here.
I noticed that most of the weights on the mouth were assigned to (IIRC) the belly and the chest. I tried weighting them all completely to the belly but it still looked weird and didn't all move as one, then I tried weighting them all to the chest, which appears to be far better.