After some time, I took another look at the issue for (actually, the two!) HR215HXAs I own.
Long story short, it WAS the cable that needed adjustment ...
Short story long ...
For whatever reason, the official instructions (in my owners manual, no less) didn't work for me. Either that or I misunderstood them. Probably the latter. See? I can't even be bothered to re-read them again before posting a followup here.
My notes, observations, and "what worked" for me (and, you?)
When the blade and transmission engagement levers are both at rest, moving the orange trans speed lever really does nothing to the cable. Engaging both blade and transmission levers, and THEN the orange trans speed lever, moves the cable.
The entire range of creeping through sprinting is done by moving the trans arm (the one down on the trans itself) no more than about 1/2" (and probably less!) of travel.
So that was learning. Applying meant loosening the cable to open up more of the low speed range. I was able to do that for each mower, but only after making the adjustment, starting the engine to test the speed, turning it off and re-adjusting.
What happens is that each time you do that, the cable tightens up. I suppose you could loosen it a whole bunch the first time, but all of this is trial-and-error anyway, because ...
... You're supposed to align the marks at the trans arm and the trans housing. But this is actually a fine adjustment, so "marks aligned," but the lines are a good 1/8" thick, may or may not actually result in enough slowness on the slow end of the scale for you.
I like mine adjusted so that the slowest speed is barely a creep! That way, when you're angling around a bush or tree, or burrowing through some tough stuff, you can just crawl around it if you need to. I still have plenty of speed on the top end.