Your comments

Just discovered an alternative: dragging/dropping the filename between groups in the sidebar. I'll give it some use to see if doing it this way will satisfy my needs.
Context menu might not be bad. I'd think that the modifier key idea would be easier to implement, though.
The keyboard shortcut works well when you only want to move one tab, but not so well when you have multiple tabs to move. And during the time I am doing this, I'm already working with the mouse.

Thanks again for contributing. It really helps to see other points of view. Jon is pretty amazing, though, so maybe he can figure out a way to satisfy both use cases!

Edit: I'd be satisfied with a key modifier on the drag/drop. If I hold down SUPER while dragging, it would use the whole pane as the target. No key, no change in behavior.

Thanks for the input, Keith. I actually thought the same thing after I posted. Personally, I don't drag and drop tabs to create new windows, so it wouldn't affect me at all. But I have no idea how prevalent that use case is. Do you do it often?
@Dave Sanders,

If you haven't found it yet, you can try DetectSyntax[1], a plugin I created (based on what @Jean Mertz did) just for this use case.

Why would this get down-voted? Aren't options good?