You have to hope that whoever did the cabling, did this in a logical manner, that might make the job a little easier. Your question “Besides manually visiting dozens and dozens of ports with a laptop — what are the options?” I afraid that is really the only option.
What you could do is get a 48 port Cisco switch, or any switch that sends a message when a port comes up, connect a PC to the console port, and patch each ethernet port to the corresponding port on a patch panel (1 to 1, 2 to 2 and so on). Then you can go around and plug in another laptop into the ports in the rooms. The console messages will display when the ports come up as you connect the laptop. Then note down the corresponding port in the room to patch panel port number. It is better with two of you, and use walkie-talkies if the patch panel and room are to far apart to shout to each other. Then you will know when it has registered the port, and you know all are working. If there is equipment already plugged in, disconnecting will identify in the same way. Document and label as you go.
No real short cuts, unless you discover the logic, and no real tools to help. Maybe worth unscrewing a couple of the faceplates to see if the cable is marked, but I wouldn’t hold your breath.
At least you only have to do it once, and then you can mark up a set of building plans and the next time will be much easier.
Check out the LanSurveyor tool from SolarWinds. Good stuff for network management!