So I don't know why this crap is happening again, but when I press "P" to open the player list, my game crashes.

That must be specific to either your server or possibly a hot key? I press p to get the menu up regularly and have no such issues.

Perhaps you have assigned a hot key which no longer works and is causing a confliction.

I had to delete and reinstall Origins to fix this.

Did you try and verify through Steam? It sounds as though you were either missing a file or had a corrupt file. Glad you got it sorted though