Sminky, after much cogitation and trial-muttering to myself, I have to deny (as to myself, at least) your premise as to "dthen".   There are probably a very few circumstances in which that little turn before "th" occurs, but far from normally.

After a little silence, and with a fresh breath at the beginning of a new sentence, there is sometimes a tiny puff of air preceding "then" to begin a sentence, which might answer to your "d". Sometimes, I say. I haven't identified any other circumstances, although there may be some.

Dave Oesterreich