The mapping of vertical scroll to horizontal scroll is something that should be done by the browser when using a multi-column layout.
My most recent attempt is this:
Right after the title there is a checkbox, checked by default, that when unchecked will lay the document out with multi-column chapters and horizontal scroll inside a chapter, vertical scroll to move between chapters.
I use a touchpad which allows horizontal scrolling so there is no need to remap v-scroll to h-scroll, but that would not work with most mice that only have a plain scroll wheel.
In practice, I too find the cursor keys (also try page-up/-down) the most comfortable way. It’s still jankier than it should but I hope that browsers’ handling of CSS scroll snap points will improve.
Although the multi-column layout works well for me, it does not for most people because of limitations in both the browser and their input devices, so I had to make single-column the default.