Just came across this thread. It can work, but..
There are a few ways to go about it, which I'll go into below. But regardless of how its done a fundamental issue will be how well the two cardioids used to produce the Side channel match each other in frequency response, level and phase. The closer that match, or the closer those aspects can be made to match before summing them to produce the Side channel, the better everything else is going to work. There are ways of getting that match close enough even if it isn't, but you will need to determine how far you want to go to achieve that.
The easiest and most flexible way of doing this will be to record the three mics to three separate channels, then produce the Side channel afterward on the computer. Not only will that not require any custom wiring or connectors, but it will allow you to improve the match between the two cardioids if required. If the two cardioid signals match perfectly (unlikely), all you'll need to do is invert polarity on the right-facing one and sum them together to produce the Side channel. If they don't, you be able to compensate for the mis-match to some extent, determine the extent of the mismatch, and determine how well this is capable of working, to determine if its worth pursuing.
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That method of recording all three mics separately requires a multichannel recorder to produce a stereo mid/side recording. Would be a good application of the three channels of a Mixpre3. But even if you don't have a multichannel recorder available, you can use a two channel recorder to do initial testing to determine how feasible it will be in practice and if it makes sense to pursue further. In the best case you may be able to use a two channel recorder (more on how you can do that in a following post)..
First, best to do an initial check of the match of the two cardioids and their sum to fig-8, which you do using a two channel recorder. Couple ways to do that.. try both!
Method A (simpler, more clear immediate result)
1) Place the two cardioids as close together as possible, pointing the same direction. I'd actually tape them together, just don't cover the side vents. Record each microphone to a separate channel as usual - you can use a two channel recorder for this if a multichannel recorder is not available. Produce a steady tone or noise on your phone and place that directly in front of the recording rig. Record some of that noise using identical gain for each of the two channels.
2) Transfer the recording to the computer. Flip polarity on one channel (normally the right one, but doesn't matter in this case). Sum the two to mono. Place the faders for both channels at 0db gain and listen to the noise. Slowly move one of the two faders.. move it up, move it down.. Search for the point where you achieve maximum cancellation of the noise that was being produced by the phone. You wont achieve total cancellation, but you do want to fine the point where the cancellation is strongest and the noise is quietest. Once you find that, note the difference in gain between the two faders. If the mics are perfectly matched, both faders will have the same position. If they aren't you'll know know which is more sensitive than the other, and by how much. At that point if you mute either channel the noise should increase significantly, but with both unmuted, the noise should be as quiet as possible. Once that's done, you'll always apply that difference in gain between the two cardioid channels which will get summed to produce the mono Side signal. More on additional ways of improving the match in a later post..
Method B (closer to the required end result)
1) Take your 180 degree angled cardioid rig outside away from reflective surfaces so as to emulate an anechoic space as much as possible. Record each mic to a separate channel as usual - you can use a two channel recorder for this if a multichannel recorder is not available. Produce a steady tone or noise on your phone and place that directly in front of the recording rig, 90 degrees off axis from both of the cardioids, and centered between them. Record some of that noise using identical gain for each of the two channels.
2) Same as before. The cancellation you are able to achieve will be significantly less, but go through the process again and see how good you can get it. Difference in gain should be the same as in method A.
Okay, let's assume the match between the two cardioids is good and you are able to achieve good cancellation using the same level of both channels with no other adjustments. That's great. It means it may work practicality without too much post work, and means you may even be able to use a two channel recorder with balanced inputs along with some creative wiring in place of a multichannel recorder.
Regardless if you end up using this for actual recording and the particulars of how you end up go about doing it, the ability to achieve a decent fig-8 null is going to be a key indicator of probable success and can be loosely confirmed via these tests. You can do them without any additional equipment, and if they work out, things are promising moving ahead..