>>299807479
>The floor base thing tilts with my head despite it being its own bone on the floor, not parented to anything. How would I constrain that?
Remove it's weight from your head bone. 
I have a feeling you made that base using something that was placed on your head or nearby before and duplicated it thus getting the weight paint of it as well.

You'll either have to do that or recreate a new floor base slimeball by making and adding a new sphere mesh instead.