Which clock did stop ?
The one running while the Amiga is one, or is it
allways starting with the same date ?
If it is the 1st you may be right with the CIA, and
you could even try to just swap CIA-B with CIA_B,
which should result in serial-probs if your right.
CIAs from A500/2000/1000(?) and CDTV could also be used.