1. I wouldn't put it in terms of time being "more fundamental than physics". We can mean two things by 'physics': the thing that is the object of study in the Physics department or the theory that gets generated by that study. Time, I take it, is one aspect of the object of study, one aspect of the natural world. So the question is: does the natural world, at the most fundamental level, have asymmetric temporal order? Or, rather, is asymmetric temporal order mearly an 'illusion' that gets explained away once you have the most fundamental picture of the world?

That's likely still unclear, but that's to be expected. We typically can't ask questions about fundamental structure without invoking that fundamental structure itself. That's why I find the analogy to left/right so helpful. We have a pretty good idea of what it means for left/right orientation not to be built into the fundamental structure of nature. And so that can provide a way of testing various claims about the fundamentality of asymmetrical temporal ordering.

2. I'm not sure I have a grip on what this additional thing is supposed to add. But I'll note that you reference 'history' and one might reasonably think that that is a temporal notion. If you meant 'history' to mean something like "the universe's extension in the temporal direction", that doesn't quite seem to allow for the distinction I took you to be trying to make.

(And, yes, McTaggert's framing is highly unhelpful.)