How was Olympic Club Swinging scored?

In all candor, I have no idea. I caution you that you should apply some skepticism toward any answer you do obtain.

The Olympics of today are trumpeted as a paragon up righteousness and correctness. That wasn't the case a century ago. Back then, the Olympics and World's Fair were often hosted concurrently in the same city. Athletes in the Olympics often thought they were in an athletic portion of the World's Fair. The Games themselves dragged on for 5+ months. The marathon included Africans who were passing through and finished in the top 10. One may have won, had he not had been forced a mile off course by a pack of dogs. In St. Louis, some events were held in a municipal park, the course marked off just hours before the events took place. If you were to imagine hastily hosting a sporting extravaganza with little time and nearly no money to prepare, you'd pretty much get the 1904 St. Louis Olympics, which were, along with the 1900 Paris Olympics, so badly organized that the Olympic movement was nearly suspended. (Source: The Olympics by Allen Gutman)

Also, record keeping of that era wasn't what we've come to expect. I just read about the first Indy 500, held in 1911. The finish was disputed because of difficulty monitoring 40 exhaust-belching cars running 200 laps. Also, the results of several laps were never recorded because an out-of-control car forced all officials to scatter as the race continued. Nevertheless, Ray Harroun was announced as the official winner and, to end all controversy, all records were burned that day. (Source: Blood and Smoke by Charles Leehrsen(sp?))

I'm not trying to equate the 1911 Indy 500 to the 1904 Olympics. What I am saying is that people didn't strictly follow procedure back then, so anything on the 1904 Olympics should be taken with a grain of salt.