I'd keep the billing address. Without it, the form would look a little suspicious. If your brand has a strong awareness and the visitors are quite familiar with your site then you might get away with it.
I would still recommend A/B testing to prove what works better for your app conversions. You did mention that you don't have a sufficient # of users however that just means that it would take longer to determine a winner when you do the A/B test. At least this way you know for sure which method worked.