I got it working! I looked at the Firewall > Log Files > Live View and noticed that there was activity on my WireGuard interface, despite there being no devices connected to the WireGuard server at the time. I knew that there shouldn't be any activity, and maybe traffic was mistakenly trying to route through the WireGuard interface instead of the WAN interface. So I disabled the WireGuard interface and disabled the WireGuard server, and it worked!
I then removed all traces of WireGuard and carefully set it up from scratch. After that, it still worked, and I had my WireGuard VPN working. I'm not sure what setting was causing trouble, but I'm glad to have it figured out and I hope this is helpful to people who might run into something similar.