I'll try to help, but I think you are over-analyzing the situation. Your positive cervical test probably was a culture, or it might have been a DNA test. I doubt it was a Gram stain only--but if it was, the diagnosis is in question. It's a very unreliable test on a cervical swab.
Oral sex is not known to transmit gonorrhea to women--that is, the source of your gonorrhea has to be a male urethra. Whether and how your partner caught it is immaterial, and I cannot speculate. It could have been by receiving oral sex, or perhaps the condom wasn't properly used. But perhaps he was infected from one of the episodes of 'rare' unprotected vaginal sex.
The other persons' test results won't change any of this. There can be false negative results with any test (slightly more often with culture than DNA test); and there also is spontaneous cure (i.e., your partner or either of the other women could have had gonorrhea but now have negative tests).
Bottom line: don't worry about which exact exposure infected you or your partner; you'll probably never know for sure. The important thing is that everybody involved needs to be treated, regardless of their test results. It would be a serious mistake for any of you to 'decide not to get treatment'.
Good luck-- HHH, MD