Thanks to an awesome individual who goes by the handle Tuia on bfmods.com, I have just patched the BF1942 server executable so that the current map no longer restarts when the second player joins.
Tuia is the same person who figured out the patch to prevent one of the hacks that was being used to mess up BF1942 servers a while ago. If you have any interest in server-side modding for BF1942, I strongly recommend that you head over to http://bfmods.com and do some reading.
I will be monitoring the server to make sure the patch isn't causing any new problems. If you see anything weird going on, please let me know. And if you notice the server restarting when the second player joins (which I'm sure it won't), let me know.