My understanding is that "progressive tax" is more typically defined as a rising average tax rate, which would make "BI plus flat tax" represent a set of smooth

My understanding is that "progressive tax" is more typically defined as a rising average tax rate, which would make "BI plus flat tax" represent a set of smooth progressive curves. It's very much worth noting, though, that there are plenty of progressive curves - including those currently in use by many jurisdictions - that have no close approximation in that set. And in particular, if what you want is an increasing marginal tax rate, it does not do that.