You may want to try something like...
Create Temporary table MyBackup
( ID as your autoincrement,
OldID as Int for backlinking/retention,
RestOfFields as their type )
insert into MyBackup
( OldID
RestOfFields )
select
ID as OldID,
RestOfFields
from
YourOriginalTable
order by
ID (this is your original ID)
Then you'll have a new table with an autoincrement with new IDs assigned, yet have a full copy of their original ID. Then, you can do correlated updates against other tables and set the ID = ID where ID = OldID. By keeping your insert via order by the original ID, it will keep the numbers from replacing out of sequence.. Ex: if your table was orderd as
Old ID = 3, new ID = 1
Old ID = 1, new ID = 3
Old ID = 12, new ID = 2
Your old 3's will become 1's, then the 1's would become 3's, and 12's become 2's
Old ID = 1, new ID = 1
Old ID = 3, new ID = 2
Old ID = 12, new ID = 3
your 3's won't overwrite the higher number, and the 12's won't conflict with the 3's since the threes were already lowered to 2's.