Thank you for giving me the opportunity to respond to your concerns. I realize I'm no great shakes as a writer.
I do try to make clear a distinction between Liberalism as a meta-ideology and liberalism as a political ideology. As I wrote, anyone who accepts that justice involves liberty and equality is a Liberal--be that person a libertarian, conservative, (political) liberal, or social democrat. Do libertarians not accept that justice involves liberty and equality? Political groups tend to co-opt key words for their names as groups. I can't help that.
A UBI is funded by taxes; a DDI is not. A UBI is 'universal'; a DDI is not (though any adult citizen could become eligible for it). Also, my paradigm had other benefits for a society that a UBI does not--beginning with eliminating unemployment and poverty. So a DDI is not a UBI.
As for the rest, one point I make in the essay is that all Liberals need to accept that they have been right about some aspects of Liberal justice and wrong about other aspects of it. I agree with you: that is a huge obstacle to overcome.