Well, I'm a stubborn *******, so at the risk of prematurely destroying the resin beads, I decided to try anyway.
It works!
First, the water coming directly out of the unit has a calcium content less than 25ppm (the drop test starts magenta and goes blue with one drop).
Second, the calcium in the pool has dropped to near 200ppm.
There were some growing pains along the way.
At first it wasn't consuming salt. Oh no! But I also realized that there wasn't any liquid in the recharge drain line. Although my little pump was capable of pulling 2.7GPM through the nearly 200' of 1/2" line, it couldn't do that and recharge. So I started closing the return to the pool when I went to bed, and opening it first thing in the morning. The softener was set to recharge at 2AM, so it got to use all of that pump's output to recharge.
Shortly after that, my $50 Amazon Special pump died. It was probably only rated at a few hundred hours.
I replaced it with a brushless pump rated at 20k hours and 24h duty cycle.
I'm hoping in another week or so to drop below 100ppm, at which point, I'll probably stop.