Definitely stay on them, or go in person if you’re close enough to the office, even if they’re saying it’s September. My recruiter thought the June board was happening, but they did end up doing May instead. Just get everything done ASAP so they can send it to Processing and get the OK.
I submitted the last of my stuff in March (I should have done it sooner and I know that’s on me), but it took Processing 3 weeks to send it back saying I had to edit some forms. So I made the edits in April, and by then it was past the deadline for May. Now I’m hoping July IS next, but if not, I only see September on the schedule, nothing in August.