This question comes up often, this time I am going to land at YUL at 00:33 and my next flight is at 16:55. Is there a hotel search engine which allows searching for late checkout? (Otherwise I'd need to ask for a "relatively cheap" airport hotel which allows for 2PM checkout and that'll be closed quick.)
As far as I could find, there isn't any search engine that can specifically find late-checkout rooms. Some hotel chains offer it on their websites or list the late-checkout in their description, but you'd have to manually go through the list of hotels in the area. For example, you can search for "Montreal" + "late check out" in Google to find some options.
Otherwise several websites offer options for booking a "day room", but that usually means checking in around 9:00 and checking out by 17:00, which isn't exactly what you're looking for. Some random examples from Google:
As suggested by @mts it might be possible to contact one of those hotels directly and arrange a different check-in/check-out time.