Let's see if I can re-put together what I did to resolve this.
Ignition on, Door closed, inside the vehicle - lock unlock on the dash, lock unlock on the remote.
Ignition off, Door closed, inside the vehicle - lock unlock on the dash, lock unlock on the remote.
Ignition on, Door opened, inside the vehicle - lock unlock on the dash, lock unlock on the remote.
Ignition off, Door opened, inside the vehicle - lock unlock on the dash, lock unlock on the remote.
Ignition off, Door open, outside the vehicle - lock unlock on the remote. (door handle does nothing)
Ignition off, Door closed, outside the vehicle - lock unlock on the door handle, lock unlock on the remote.
I think that about sums it up. Problem went away. Suspect it has something to do with the factory alarm system.
Engine was off the whole time, IIRC.