It's been a while since I deciphered the the Elk manual zone definitions, but if you set your entry door to zone 1 or 2 (burglar entry/exit) and all other doors to zone 3 (burglar perimeter instant) AND use "stay instant," you can get where you want. I don't think using just "stay" will work, since then the zone 1 or 2 entry door will arm with a delay in stay mode.
One caution: you probably want to also make sure that the "auto stay, no exit" setting is OFF (or at least know if it is ON), since if it is on, and you arm away without opening the door, the system will default to stay mode (not stay instant), and you will then have a delay on your exit door.