Update: it seems to matter whether one uses Ubuntu 15.10 or Ubuntu 15.10 minimal as the base operating system. Yesterday I leased a VPS from a host offering Ubuntu 15.10 and successfully ran aubreyja's install script. All WeBWorK features seem to be working well now, and with speed.
When the server was running CentOS 7 a day ago, I believe it was the normal version, but students were still encountering problems. I think another lesson here is that not all VPS hosts are equal. I am paying substantially more per month now (and getting less RAM!) but having a functional WeBWorK server is worth every penny.
I hope this information helps someone in the future.