You're up a creek here. The two "tracking" features are Advertising Identifier and Identifier for Vendor. The former can be reset within the Settings app quite easily while the latter will reset once the user uninstalls all apps with the root bundle identifier associated with the app suite. Both also change with a device reset of course.
If you're deploying the app with an MDM solution you will have access to that device's UDID as it still flows forward to MDM servers, you just can't access it programmatically in your code. The complete deprecation of UDID, serial number and MAC address (even with private APIs) stomped all over some custom utilities I wrote within our Enterprise to try and accomplish something similar to what you're looking to do. If you find somethingthats consistent I'd love to see the follow-up!
EDIT:
I had an epiphany while circling back to this situation again. If you are in fact using AirWatch (I can't speak to Mobile Iron, etc) you can setup the console to send a keychain value to each device at the time of app install. From there the app will be able to consume the value AirWatch sends down. The same goes for any attribute that AirWatch harvests for the device (serial, UDID, MAC, etc). While this workaround comes with a big caveat (using AirWatch for deployment) it will work. Since Apple neutered all Serial Number work arounds win iOS8 this is the most viable option I have found.