I did say this:

While there quite likely is some degree of resolvable factual disagreement about the extent of certain inequities, and maybe-somewhat-resolvable disagreement about how those inequities might be lessened, there is also disagreement about how much those inequities should matter to us and affect our behavior, both political and personal.

So I agree there are a number of falsifiable beliefs on both sides. But the mere fact of falsifiability doesn't mean the disagreements are easy to resolve, partly for "politics is the mind-killer" type reasons, and partly because it is legitimately difficult to find conclusive experimental evidence for causal claims in the social sciences.

I do, however, think there are important value disagreements about how to trade off efficiency and equity between left and right, and I also think your description of the "main value disagreement" is a caricature. I'm pretty sure I could easily come up with socio-political thought experiments where all (non-moral) facts are made explicit, leaving no room for disagreement on them, but where we would still disagree about the best policy, and I assure you I'm not one of the "pathological" egalitarians you describe (although you would probably consider my views pathological for other reasons).