I am a consultant who designs and budgets such things. If its a new door and the hardware can be specified, I would use a panic device with built in functionality. If its just a mag (delayed egress type), then your cost still sounds low.
I budget around $2500 for such doors and have budgeted as much as $20,000 (yes you heard that right) for the specialty versions; but I don't get holding the bag (usually) if that cost does not work...you do. I would give them two unit prices so you don't look like you milking your customer: one for the work at the door and connection to the system (because that is a relative constant); the other for wiring, conduit, etc based on a liner foot pricing, which can be field verified if needed. This could also be done with things like, power supplies, additional IO boards, bucket trucks or lifts, etc. Just make sure you define what EXACTLY it is your unit price includes and make sure the Customer understands and agrees. I would not ask an integrator to do this without giving him some wiggle room unless I was absolutely sure each and every door was the same (I cannot think anyplace where that would be the case).
Looking through your eyes, i can see many reasons why integrator's don't like unit prices, even though i call on them to do it many times. If this is a good customer though, and a reasonable person, you should be able to work through the issues. Just make sure you and he/she are on the same page.