I agree with your reservations with originalism, but I think the debate between originalism and living constitutionalism is really a red herring.

Hard constitutional cases aren't hard primarily because of ambiguities that could be resolved by appealing to the Constitution's "original meaning" on the one hand, or contemporary understanding on the other.

Hard constitutional cases are hard mainly because the Constitution embodies many social and political values, and those values often come into conflict with one another. When they do, the Constitution itself doesn't say which value should yield. Judges are forced to prioritize or seek some balance if possible.

Take the abortion example. The Constitution clearly grants the government the power to legislate for public health and safety, but it just as clearly creates a zone of autonomy and privacy around the individual. How do you balance those values? Simply saying that one of them is entitled to no concern at all (as opponents of Roe would like) isn't a realistic option, but neither is saying that the state has no interest at all in unborn life.

And hard cases are hard sometimes because the meaning of the underlying facts can change over time. In his 2010 Harvard Commencement speech Justice Souter gave the example of Plessy and Brown as two cases with the same basic underlying facts, but in which the court reached different outcomes not because the Constitution's meaning had changed, but because the meaning of the FACTS had changed. Whereas segregation might have seemed enlightened relative to slavery in a time where many people could still remember slavery, by the 1950s it was clear that separate was inherently unequal. Social facts have social meanings that change with time, even if the meaning of the Constitution doesn't, and that can force courts to reevaluate precedent.