SOLUTION:

I brought this up in another thread, but that covers other issues, so for details that aren't here, you can check there.

I solved this on the dhcp server (dnsmasq). Oddly enough, even though I was specifying to use 172.16.7.17, somehow it was being read as 172.16.7.174. I have no idea why, but that was in my reserved range of IP addresses to not give out, so the dhcp server was having issues with that and not giving it to the Pi.

I changed and ended up using 172.16.7.11 instead of .17. After I changed to that, allowing time for propagation, it worked out.

It is puzzling, since the dhcpcd logs on the Pi say they're being offered 172.16.7.17, but the server says it's .174 instead of .17. I have not tried to change back - I don't want to deal with that again. (I'm wondering if something was glitchy when the dhcp server wrote the config file to the drive.)