If anyone can point me to any online writings on the subject which tackle the standard challenges to libertarian capitalism in a way that doesn't hinge on deontological ideas or ideas of deserving, I'd be interested to read them.

No strong opinion on whether they're correct, but from what I've seen libertarians argue from consequences rather than deontology most of the time, so I have to wonder where you've been looking. As for pointers, there's a libertarian-leaning econ encyclopedia here.