This may be late for this topic but for any others researching.
The only way you can do a delayed egress lock is to purchase a locking system that was manufactured for this use and sent through a Nationally Recognized Testing Laboratory and that has been listed for this purpose. Using different parts and making your own is not legal. It is an excellent way to kill people, have your insurance deny claims, and possibly go to jail. I highly recommend you seek the help of a professional access control company.