David came up with an interesting observation, but it didn't seem to help with Nils's problem. But, there's more than one way to skin the cat: using David's observation, and the fact that changing the "middleCPosition" property doesn't make the clef get re-drawn, we can trick Lilypond into drawing a tie between notes which appear to be different enharmonic spellings.
Do you prefer this way, Nils? You don't have to muck around the changing the shape of a slur.
Regards, Bruys
\version "2.12.3" % ties work between notes with same name, even though the position
% has changed, e.g. { c'2~ \clef bass c'2 }