Well, since I have backups of everything anyway, I decided to hack at it…
I first removed the new "NRPE" package. My plan was to go in and hand-edit the XML file after that to remove any traces of NRPE/NRPEv2, then restore it, then re-install the new NRPE package, and then if possible copy-paste the relevant part of the config back from my NRPEv2 configuration, and if not, go in and re-enter everything via the gui (ugh.) However, simply removing the NRPE package actually cleared up the broken NRPEv2 menu items. I then backed up and hand-edited the XML file. The only thing related to NRPE that I could still see remaining in the XML file (other than firewall rules I had created) was the orphaned configuration for the NRPEv2 service (exactly the part that I wanted to try to save), specifically:
pfsense -> installedpackages -> nrpe2 -> config
So I carefully cut the "nrpe2" and below branch out of the XML file and reloaded it. Then I reinstalled the NRPE package using the package manager. Then I backed up the XML file and took a look at it again to see what changes it had made. I discovered that the new NRPE package actually uses the same "nrpe2" stanza in the config file (so I'm not sure why it wasn't working before), specifically, pfsense -> installedpackages -> nrpe2 -> config. So this time I replaced that branch of the XML with the one I had backed up previously, saved and rebooted yet again, and now everything seems to be back to normal. So it must have actually been something else somewhere else in the XML that was gummed up, which installing, removing, and then reinstalling the NRPE package fixed. Sigh.
Interestingly, the new NRPE package actually is referred to as "NRPEv2" in the menus and such, so... shrug. I have no idea why all this happened. It seems to me that even if the package were removed and then later reinstalled, that the XML wouldn't get all bungled up like this.
Annoying to have to go to this much work to clean up after an update, but at least my router is working again!