Alright, I prepared a simple script that does what I want.

I was hoping there would be an easier way.

Is there a way to export files from a .blend with a complicated collection structure with a sub folder for every collection level? The add-on allows for a custom sub folder to be defined per object, but there's no way to bulk-assign it.

I think what you're looking for is $glossiness, not $glossyness. Could that be the issue?
https://developer.valvesoftware.com/wiki/EyeRefract

Eyes are a pretty complicated topic to deal with. There is some scarce documentation available on the Valve Wiki.
https://developer.valvesoftware.com/wiki/Eye_Position_Setup
https://developer.valvesoftware.com/wiki/Eyeball
As far as I know no such option as $glossyness exists, where are you editing that?

Which game is the model for?

I do believe that SMD supports the influence of maximum 3 bones per vertex. Could this be the issue here?

Happy I could help.

Are you trying to rotate the bones in Edit Mode or in Pose Mode? From the image it seems that you're trying to rotate them in Pose Mode, in which case:
First, you need to set the Transform Center to be each individual bone:
https://i.imgur.com/t4zBZu0.png
Then you need to set the Transform Orientation to use the bone's local axes:
https://i.imgur.com/fnk7LBw.png
Then select your bones, press R to start the rotation then press Y to make the rotation only around the Y axis(parallel to the bone), then press Y again to make it so each bone is rotated individually.

The fps.dmx error is very common even for me and I'm not sure what exactly is causing that (or why it's needed in the first place). The other file migh be the culprit since it seems to have a messed up file extension.