I suspect you meant billing plan type. "Billing type" can be easily misinterpreted as the corresponding billing document type.
There is only one billing plan type possible for the sales document type, but the billing plan can also be assigned in the item category. This information can be easily found in SPRO.
To be honest, I don't understand what's a big issue with having a different sales document type. It's just instead of making a decision on the second screen the users would need to make it on the first screen (by choosing the appropriate type). The business process is a bit different too, so it seems hardly justified to mix those in a single document type IMHO.