There’s not really anything special about that rig:
You have armature-level transformations in that file, which won’t get exported and maybe will screw things up. First thing I did was to clear rotation, scale, location on the armature object and delete all keyframes for those.
Then, I used “create model” from sidebar/MMD and joined your armature to the new MMD armature. I made a few cubes so I could see that it was working and exported the model, then exported the animation. Looks like it’s working fine.
That leaves you with an extra bone-- the one generated by MMD Tool’s new model-- but you can delete it if you want. It’s not really doing anything.
If you want the armature level transforms (well, the translation and the rotation) in MMD, you’ll need those to be on a bone rather than an object. I’m not sure the best way to do it-- best would be to directly copy your armature transforms onto your root bone. There are plenty of ways to do it with baking animations, but it seems like you should just be able to copy/paste keyframes-- I just don’t know how to do it, in the case of copy/pasting from armature->bone.
Note that MMD doesn’t support bone scaling (or object-level scaling at all, not outside of .x files, and even then only uniform scale) and so no animation using scale is going to work in MMD.