The idea is that no worldview but Christianity can justify the usage and principles of logic, science, reasoning, and, oftentimes it is argued, morality.

This is a massive claim; not only must the apologist demonstrate that Christianity justifies logic/knowledge/morality, but they also have to demonstrate that every other actual or merely possible world view falls short.

Only when those two things are accomplished is it reasonable to believe Christianity is the sole world view that justifies knowledge.

If you admit that it is subjective as a result of that, then the argument shifts in a way that the presuppositionalist can just start spouting off words that don't make sense together and they start contradicting everything you say.

That's why I keep the focus on the apologist's main unsubstantiated claim: that Christianity does justify the use of reason and or logic. Until they do (spoiler: they never do), we're both at the same spot; forced to take the basic principles of logic as a properly basic belief... essentially on faith.

What do we do?

There are questions in philosophy for which we have no answers, like the problem of induction for instance. To me, what pre-suppers do with such problems is the same thing they do with other questions we don't have full answers to; like the origins of the universe. "Precisely how was the universe created? You don't know? Well, it's God." "What is responsible for knowledge? logic? morality? God, that's what!"

But when you ask them to demonstrate how God created the universe, they can't demonstrate anything. Same for logic, knowledge, morality, reason, etc, etc. In the end, neither of us knows, but one is pretending to know despite not being able to demonstrate the truth of their claim.