Hey, I'm just stoked some tapers such as yourselves are finding these alternate approaches as valuable as I have!
I suppose the main working premise for selecting the optimal forward facing center microphone for these configuration should be choosing a microphone which is "as directional as possible, while still playing nice". I currently think of the roll played by the center forward facing mic mostly as "surrogate for SBD", which may help explain the motivation for using a highly directional mic there as a way of focusing on getting the clearest direct sound from the stage and PA, while excluding as much audience noise and hall verb from that channel as possible. I feel the directional-as-possible part is firmly established at this point, and it's the "still playing nice" part which isn't as well defined. In my experimentation over the past decade, I've moved from using a center omni to using a slightly more directional sphere mounted omni, to a cardioid, and on to a supercardioid. A supercardioid, which is the most directional first-order pickup pattern available, is the most directional pattern I've tried. Moving further to an interference tube "shotgun mic" trades some of the the well behaved off-axis response of a supercardioid for further increased isolation. I've yet to get a firm feel for where on the continuum pursuing further increased isolation in the center channel becomes overshadowed by increased off-axis coloration and timbre problems of using a shotgun, which is a determination that is always going to be somewhat subjective. Is more rejection actually needed? How bad is too badly behaved? Well it depends both on the situation and the esthetics of the recordist.
Rocksuitcase's and Kindms's recordings using a ck8 shotgun in the center mic roll are helping to explore that territory.
With that in mind, perhaps the second part of that center mic selection premise should be the realist's take of- "usually best to use your better sounding directional microphone". If you have a great cardioid and a crappy sounding shotgun, you'll probably get better results using your better sounding cardioid. But fortunately here's something I've also found to be true- a well designed multi-microphone configuration can take some of the pressure off having to use a really top quality microphones all around the array. Using just two mics places lots of responsibilities on those two mics, and its harder to escape the need for top quality microphones. They need to do a large number of different things well. In these multi-microphone stereo configs each mic position represents a more specialized job, with all the mics working together as a team, partly covering for each other's weaknesses. Four reasonably strong players can beat two superstars. But the coaching decisions become more involved!
I've said it before here, but I think it bears repeating that audience recording is an odd bird in the music recording world. What concert tapers do is not closely related to studio recording at all, nor modern classical and film-score recording, and most sources of recording information available on the web or in books doesn't really apply directly. It's perhaps closest to what would now be called 'minimalist' classical recording as it was done over half a century ago, even though the situations are very different and the gear is almost entirely different.
These multi-microphone configs intended primarily for outdoor audience recording and I suppose best described as spaced pair plus center microphone configurations, are a sort of mindful combinations, evolutions, and blendings of a few different approaches. The starting point is two wide spaced mics at least 3' apart. From there there the main influences are a bit of Decca tree (3-omnis in a triangle), a lot of OCT (two sidways facing supercardioids with a cardioid in the center), informed by a lot of Michael Williams' multi-microphone array design (extensions to his original Stereo Zoom 2-channel ideas), all greatly influenced by David Griesinger ideas on multichannel recording and acoustics. I've just worked to modify and adapt that stuff to the unusual backwater application of live music audience recording.