As others have said, the profile guidelines come from the Cayman Watersports association. So any operation you ask openly will repeat those numbers back to you. However, shore diving, you are under no restrictions other than dive your computer and take a dive flag buoy with you. With all that said, I have dove many times with Reef Divers, with many dives quite a bit longer than 60 minutes and have never once been reprimanded or asked to shorten my dives. The way to make sure you can maximize your times is to:
1) Convince everybody on the boat to be either on-time or preferably early to leave the dock. If they ask you to be on the boat at 8:15, make sure everybody is on the boat and ready to go then, not on their way down to the drying room to get their gear together "around 8:15ish". Being on-time leaving the dock allows them more freedom to allow extended dive profiles without getting back to the dock late for lunch. If you leave 15 mins late in the morning, they have to make that up somewhere or get yelled at for being late for lunch. They will either do it by going to sites closer to the resort that require a shorter boat ride (but may not be the best sites) or by being stricter on getting people out of the water.
2) Be among the first into the water if you want a longer profile...that way you can come up around the same time as everybody else but have a longer dive. If you dilly dally on the deck and drop in 5 mins after everybody else is in the water, Doing a 70 min dive is going to get you scolded because you will likely be up 15 mins after everybody else is on the boat.
3) Regardless of #s 1 & 2, get close to the boat before your dive is finished so you can see when others are going up. If you are passing 60 mins and there are still lots of people milling about, you are fine. But if you hit 60 and you are the last ones down, it is probably not a good idea to stay a lot longer. However, the dive crew will be much more lenient if they can see you from the boat and know where you are. If you are down after everybody else and they can't see you, that is when they will get nervous. When they get nervous, they will be more likely to look hard at your computer when you do eventually surface.
Bottom line is that if you are respectful to the dive crew and the schedule the resort sets out for them to follow, they are very likely to be respectful of you and allow you limited freedom to dive longer profiles. If you flout their profiles openly and do so in a way that causes them problems, you are likely to get called on it. Most of all, don't surface with your computer in deco or with an empty tank. Both are things that will either get you taken out of the water or at least sternly warned about their rules.