I actually attended the SF one a week ago. I have some suggestions, but there could be other better ways so don't take my word for it!
-Find out the max occupancy for the room, and it'll be your choice to either to team people up randomly or teams selected themselves. personally, i think it's good to let people figure out how big their team will be, but it'll be good to limit to number to maybe around 5-7 people per team and no more than that. You should also have an option for people to team up with other strangers just in case there are people attending the event alone.
-Locking the door is a fire hazard, and I believe it's illegal as someone said in this thread. a solution is to just to hire someone to guard the "exit" and act as a door. Meaning that when the team finds the key or the code/solution for the "door," they just tell the solution to the hired person guarding the door. If the answer is right, then the team "escapes." So basically, you'll technically still be locked in, but instead of a door, it's a person guarding the door.
-Make the puzzles moderate or hard, and but also try to make them simple, but don't make anything that is unbelievably impossible to solve. Personally, I don't advise math problems unless they are simple and in the easy or moderate level. Think of puzzles that really make you think outside of the box OF the box. lol Only stick to puzzles that have common knowledge or with knowledge that people can obtain from the event itself. In other words, if you use information that can only be obtained from outside of the game, people with smartphones have a great advantage since they can probably look up the answers from their phones. Don't use puzzles that require knowing addition information that some people will probably not know.
-If you want different sessions to accommodate more people, 15 minutes isn't too bad, but the set-up can be a hassle depending on how the puzzles are like and the amount of people attending (I'm sure there will be a lot because escape games are pretty famous). Just make sure you are FULLY organized on that, and I mean it. Like if you're going to make the players open up a chest with a number combination, always double-check if the combination is correct. You probably know what I mean. You also don't want the event to be running on a late schedule. The easiest way to avoid this problem is to just make one big session that accommodates a huge group of people in separate teams, and make them stay in one big room (which is the panel ballroom). If you know you can pull off keeping the schedule organized and on time, then go for it. Don't plan on risks.
Anyways, these are just my suggestions for now (that I pretty much thought of from the top of my head). GOOD LUCK on this! I actually would love to attend this panel.