Hi! I'm Emily and I came across this forum and I wanted to introduce myself because I'm the author of this Reddit post. I'm glad to hear that it's been helpful!
I'm originally from Canada and I moved to Paris specifically for Notre Dame and to, quite literally, pursue a career as an expert in all things Notre Dame - or, as I like to joke, “a professional fangirl”. I'm a self-employed tour guide giving private tours that focus on the cathedral's architectural history, the restoration and its role in art, media and literature.
At the time of this forum post, yes, there were issues with the reservation system. But luckily, it seems to be working more smoothly now, than when it was first launched! The auto-refresh functionality is working again, the wait time in the virtual "waiting room"/queue to enter the system has reduced significantly, and openings for new time slots are more evenly dispersed!
And yes, new/additional "same day" time slots are released 4 hours in advance. For example: At 5:00am (Paris time), new time slots are released for 9:00am for that same day. At 5:30am, new time slots are released for 9:30am, etc. However, there are certain hours when no time slots are ever offered, therefore no new time slots are released 4 hours in advance of those hours. For example: No time slots are offered at 12:00pm, therefore no new time slots will be released at 8:00am. The availability of these time is still subject to the current available capacity inside the cathedral.
There's truly nothing I love doing more than sharing my love and knowledge of all things Notre Dame. I'd be more than happy to help if anyone has any additional questions about visiting Notre Dame!
(Please let me know if this comment breaks any of the Community Guidelines and I will edit/remove if needed)