AFAIK the paralysis argument is about the implications of non-consequentialism, not about down-side focused axiologies. In particular, it’s about the implications of a pair of views. As Will says in the transcript you linked:
“but this is a paradigm nonconsequentialist view endorses an acts/omissions distinction such that it’s worse to cause harm than it is to allow harm to occur, and an asymmetry between benefits and harms where it’s more wrong to cause a certain amount of harm than it is right or good to cause a certain amount of benefit… And if you have those two claims, then you’ve got to conclude [along the lines of the paralysis argument]”.
Also, I’m not sure how Lukas would reply but I think one way of defending his claim which you criticize, namely that “the need to fit all one’s moral intuitions into an overarching theory based solely on intuitively appealing axioms simply cannot be fulfilled”, is by appealing to the existence of impossibility theorems in ethics. In that case we truly won’t be able to avoid counterintuitive results (see e.g. Arrhenius 2000, Greaves 2017). This also shouldn’t surprise us too much if we agree with the evolved nature of some of our moral intuitions.