Thanks for taking a look!
I went through and made sure that all of my vertices were assigned to a vertex group by selecting every vertex in each vertex group manually, then Ctrl-I to invert the selection. There weren't any unassigned vertices I could see -- just to check, I deleted selection and saw no difference. Are they perhaps misnamed? The base unit I used was the Danish Berserker, for reference. I used Bone Weight Copy to get the vertex group names and (most of the) vertex assignments for them. I also deleted everything but Base HumanNeck1 and Base HumanNeck2 for the head, and deleted those two for the body. Unfortunately, still no dice.
What would I need to do to correctly assign the groups from this point?
I don't know what went wrong as it all looked good to me and I could not get it to export either. But I was able to export it to .fbx and re-import the .fbx into blender and then after a bit of tidying up I was finally able to get it to export to .br2 (attached).