But if you call the lens cap exposure 0.0 on the x-axis,...
Hi, this seems to be the only real issue. But when I looked through the section, I don't see that Henry actually said this. (If he DID, this would be improper; using the log axis does not allow for plotting an exposure point with zero light, which is what a lens cap should ideally produce.)

So I don't see anything wrong. It looks like he simply plotted the actual exposure steps down to the point where they don't change anymore, which should be the same density as the lens-cap exposure. But it's not actually the lens-cap exposure which is plotted. As he said, the lens-cap exposure is a reference for base+fog, and I as I read things, that's all it is.

I think this is the only problem you have, right? Otherwise, it's ok to use any value one likes as a starting point on the log exposure axis.

(note for other readers: it's page 144 in second edition, Richard Henry's Controls in Black and White Photography)