The phantom adapter is providing required power to the electret mics. This power is for electronic inside mic, specially for FET. Different mics have different FET and electronic inside, so they are using slightly different powering.
The best is use phantom adapter that is designed specifically for your microphones. If you use a different brand of the power supply, it may happen that the microphone signal will be distorted (because FET is not powered properly, it can happen probably at higher volumes). If you want to be sure, use original - you already have it or Naiant adapter. Remember that all adapters are around three inches long.
Edit: Be careful, non-original phantom adapter can destroy your mics too. Before trying it, measure the voltage of non-original adapter and compare it with your original adapter. Naiant adapters are ok, he is designing it for specific microphones.
The second option is to use your AT831 the same way you are using your CA11. Somebody can terminate it to stereo jack with mod 4.7k. One alert - 4.7k mod will decrease signal of mic about 12db. If you want to record quite acoustic shows, ask somebody to make you switchable 4.7 mod to turn it on/off .