Apart from that, I went back and looked at the Dowek, Hardin, Kirchner, Pfenning paper again and realized that the obstacle I wrestled with those several months ago last time I seriously thought about it might be really easy to clear. All I need to maintain is weak normalization, and I can get around the apparent necessity of a WN-destroying rule that "reduces" any irrelevant cons in a substitution to any other well-typed term by just "baking in" that rule into VarShift and Scons. Not that the non-left-linearity of Scons doesn't still look kind of extra-shifty in the presence of dependent types, but I'm willing to accept it for now.
I did leave "Sequence" in the lounge. Better for it to get played there than collect dust in Florida.