Tentatively, I seem to have found a solution.
Before, I had largely used the R installation from Anaconda using its default channels. The only exception to that was when I upgraded RStan to 2.19.2 in a failed attempt to stop the crashes; in that case, I uninstalled the conda packages r-rstan and r-stanheaders and then installed the rstan and StanHeaders packages using install.packages() instead.
However, if I used the R installation from the Conda-Forge channel (in its own conda environment, BTW), then RStan seemed to behave properly. I’m not sure why that makes a difference, though I notice that with Conda-Forge, the CLang version is 9.0, where as in mainline Anaconda, it’s only 4.0.