Island vs. Event

You can still enter the island, joe is gone and people on the island got removed in the maint, but you can still return and stay just fine. (Keep in mind, the event page mentioned nothing of this at the time of me writing that post the event was still going on.)

To add on to this, after the event the flight action was disabled, but as said here, that is a glitch that will be fixed, it is meant to be kept after the event.

Did KR players petition for Doki Doki Island to be permanent for them?

Not that I know of, I'll ask a Korean literate person to look into it.