Found a solution, in this:
\override TieColumn.tie-configuration = #'((3.5 . 1) (5.5 . 1))
It’s not as precise as I’d like to be, but it gives me this, which is clear:
I’d prefer to have the direct control, but as that appears to be buggy (and not just counter-intuitive), this will do well enough.
I’ve logged the really bizarre behavior I encountered earlier as a bug.
Thanks for those who offered help.
-Arle