We did the MK 'til 3am thing during Spring Break - the week leading up to Easter. And, so did at least 30,000 other people. It was astonishing that there were that many people willing to stay up that late. But, that's Spring Break for you. The last attraction we went on was Space Mountain. We got in line at 2:30am. We exited at 3:10a. Both sides were open and there was no FastPass to bog down the standby line. Still, at that time of the day, the line extended well out of the attraction and toward Astro Orbiter. The posted wait was 50 minutes. AT 3 AM!
I'd really love to do a super late night at MK when it's not quite that crowded. Perhaps that early June date is the ticket.