Oracle Enterprise Manager (OEM) locking SYSMAN account
Benoit, you actually had a partial answer, everything you said was correct, but after next reboot, the account locked. After several hours of more research, the following issue was discovered, with the appropriate resolution.

Enterprise Manager had the default SYSMAN password stored for its credentials, and was trying to lock in with that password in rapid succession (300 times a minute or so according to the Event Log). Hence, after several rapid tries with the same wrong password, Oracle locks the account.

Setting a new password in SQL*PLUS or SQL Developer doesn't reset the password used to login to Enterprise Manager, to reset the password in enterprise manager, you need to open a command prompt and do the following:

emctl config oms sso -remove
emctl stop oms
emctl start oms


During the above commands, it'll prompt you for the current SYSMAN password, which you can enter, and it should remove the SYSMAN password used by your Enterprise Manager Console, replacing it with the one you just entered.