does his ability prevent someone who shoots him with HLC from changing crits to hits?

I would say that it probably does not. The change of the dice is a "must" and it is done before the modify dice step.

I've seen this discussed before. I believe it is doll considered a dice modification. So if that's the case, then it is one specific unfortunate card interaction. The rule still applies to rerolling and focus as you'd expect, though.

HLC kicks in immediately after rolling, before dice modification.