First off, I make no warranty of any of these suggestions. Especially if this is actually a bank...
I would be hesitant to completely rely on an all-electronic solution, since if there is a failure (which, frankly, is likely with a budget of only 200 per lock), you don't want to have to resort to a plasma torch or something to cut open (and destroy) the door to get in.
What seems like an interesting option to me though would be some of the RF-controlled keyless locks on the market. These look like a normal deadbolt, but have an RF remote.
What would be needed in whatever is chosen is the ability to hook into it, specifically, you need two things:
- The ability to remotely control lock/unlock
- The ability to sense if it's locked or unlocked
I'm going to assume that you have some type of microcontroller running the rest of this setup. You didn't specify.. but presumably you have something that has some I/O on it, the ability to connect it to the locks, and some software running to handle what I describe below. I'll also assume that you have an alarm and monitoring.
To control the lock, ideally, you could hardwire in to it, and be able to apply a signal to lock/unlock all the deadbolts. Less ideally, you could hack apart the remotes, and have your controller effectively press the buttons on the remote(s) to lock/unlock. This adds unreliability since you're dependent on an RF signal.
Since these are keyed locks, you have a nice backup mechanism if everything fails: use the 4 keys to open the locks (and note, you'd need to be sure they're 4 separate keys).
Of course, since they're keyed locks, they're also susceptible to being picked/bumped. To try and combat that, what you can do is have your controller monitor each lock individually. If any of the locks ever open when the controller didn't tell them to, then it should trigger an immediate alarm (consider: someone is likely to pick/bump one at a time). If this is an exterior door, then this is your first line of defence, unfortunately. If it's an interior door, then you should also have motion and other door sensors that will hopefully trigger before someone gets to this door.
You also need to consider all other aspects of physical security. You're only as secure as the weakest point, so if someone can break through a window or wall or vent then it doesn't matter how good the door is. Physical security is also just a matter of time: eventually, you can get through anything. That's why I suggested having an alarm system connected, which is both a deterrent, and triggers a police/whatever response. Consider: safes, even high-end ones, are rated by the time it takes to crack them: your door will be no different. Having video cameras probably helps as well, both as a deterrent and to help catch people afterwards. Your video and security system also need to be protected, so that they can't just be disabled/destroyed.
On the other hand, too much security and you actually can attract attention. I've heard that the houses with extra locks, security cameras, etc, are often targeted by thieves since they look like they have something valuable worth protecting.