@agraham : Considering your experience dealing with large companies, got any comments on this post?
The suggestion adding their branding, at low cost, is a good idea. It does help to ensure that those purchasing, and those who will use, the item perceiving that they are using something that is part of their business. It also might help to stop the app 'creeping' elsewhere.
I thought a bit about the licence/inventory problem and, depending upon how you perceive them as a customer and would do one of two things
I could just pass over the apk for side-loading, and if they lack that expertise, charging for your time to train some of their employees how to do it and keep account of the number of times they do it. They would just report, or you would request, every month or so how many devices they have produced. Remember they may well, as good business practice, have their own inventory control for the devices as they are a business asset so you could piggy-back on those procedures.
Or I might build in a simple activation scheme that uses a master device to produce an activation code for each install and keeps count of the number of activations - it could even send you an SMS or email for each one if you get really paranoid. The activation doesn't have to be bullet proof, as I said above this is a business relationship not a retail one. Every time it starts your program would check for a private file with its activation code and if it doesn't find one displays a device ID to the user to enter it. The installer has a master device that takes that ID and encrypts it and display it to the installer who then enters the code into the newly installed program that saves and decrypts it, and if the ID matches it is then operative. This suffers the usual problem of both master and installed program having a shared encryption key in their code but it doesn't have to be a clear string, it can be built programmatically and so when obfuscated would not be easy to find. But anyway this is for inventory control, not protecting Fort Knox, so it only has to be good enough!