Whether timing the start date at the new company for the very end of the 60-day grace period would cause any problem for the PERM process
If going to Korea would be a problem, I’d like to stay in the U.S. and take some time to rest instead,
and I’d like to know if timing my start date at the next company for right around the end of the 60-day grace period would cause any problem for the PERM process.
PERM processing and the Grace Period are unrelated. Later, when your unlawful presence period is calculated, if it exceeds 180 days of unlawful presence, that becomes grounds for denial. The grace period is simply a period that allows you to postpone departure a bit, even though your status has already technically expired.