I think left-to-right works in this case because my target audience is the everyman, not only technical or highly-educated folks. In my experience, people care mostly about the meaning of the information and don't care much about graphs or data in themselves. In that sense, I think of this kind of graph as more of a word or a sentence than a traditional graph, and mostly we read words left-to-right.
Because this is backwards, I'm trying to figure out what I'm missing. Am I supposed to be thinking backwards in time? I get confused on what I'm trying to get out of it, decide I don't understand what you're talking about, and move on. Just my $0.02.
The less people have to relearn the easier it is to get them on board, all else being equal.
The key here is that I've integrated this particular type of graph as part of a larger interactive visualization or UI. Within that larger system, the graph is generated in real-time in direct response to your input about your own behavior.
I put up an interactive demo here: https://benome.ca/Intro/
So in the intended context, graph's meaning is more clear than it appears at first glance. But in any case, it's easy enough to switch a graph's direction.
As you say, the norm is right to left, highest priority (now) on the far right, like this: https://square.github.io/cubism/
It must be an acquired taste, or contextually dependent, because even though I do plenty of metrics visualization which is right-to-left, left-to-right for a high-level view of behavior feels fine to me.
But your graphs go right-to-left!
Being "now", it's always changing and thus everything on the graph - one's past behavior - gradually moves to the right.
Check it out here: https://benome.ca/Intro