You can try this (it has worked before)
1) Convert timestamps to strings (ALTER TABLE …)
2) Do Sync
3) Convert strings back to timestamps.
1) and 3) can be done from jobs running in same batch as the sync job.
Basically a MySQL timestamp is stored internally identically as is a char(14) … like 'yyyymmddmmhhss' or '20051202003145' so the conversion forth and back should be pretty straight.
But of course any application/script that makes use of the timestamp will fail. So in practice I think it would be wise somehow to block access to the database for other apps while the process is running