My first inclination is to treat this like mic'ing a percussionist with a pair of spaced overhead mics. I have tried this and found that some of the bowls just were not picked up as much. Either they were too faint or too much. I suppose if I could setup a projection response setup to see which ones project better then I could setup according to what the bowls put out. Different bowls project the sound waves in different patterns. Some out of the top more, some off the sides more. So if I can determine which is which (some I already know) then I could lay the bowls out in a more optimum arrangement so as they will still sound good in the grouping but be laid out better to be recorded.
Simplest will be two mics suspended overhead, spaced apart so as to have approximately equal pickup of the the bowls to either side. Basically just above and a foot or two away from either side of your head, and out as far in front of the gongs as from the bowls on the floor. That will achieve a natural live sounding ambience as well as an even stereo pickup of all sound sources, including the flute, your chanting and whatever else you choose to do. Ok, I can try that again. I have on a couple setups with mixed results, again, bowls tend to sound weak & gongs too strong.
Funny, I immediately thought about the sort of di-polar radiation of gongs, and didn't think about the vibrational modes of a bowl, which like a bell I'd expect to radiate primarily in the horizontal plane as the walls of the bowl vibrate. With that in mind I understand how many of the bowls might sound quieter and generally less solid when mic'd from above. Your empirical knowledge based on actual experience is always the most valuable information and trying things is only way to really test conceptual ideas which might seem great "on paper".
What about your cardioids spaced apart and placed low, set up to either side and slightly behind you, parallel to each other and facing forward out into the room, with their primary axis pointing across the top of the bowls. They then will be more on-axis with the sides of the bowls instead of looking down into them from above. Yes they will be more or less directly under, between, or just in front of the gongs. Inverse square law works against us this time, making the gongs louder by their proximity, but there are a few things which might work to counter that and balance that. Namely the directional pickup pattern of the cardioids and the dipolar radiation tendencies of gongs. If the cardioids are pointed 90 degrees off-axis from the gongs, the direct sound from the gongs will be picked up with 6dB less sensitivity than the bowls which are on-axis with the mics (cardioids have similar sensitivity for everything within something like a +/- 60 degrees off axis from the center-line of the mic. And they'll pick up even less if the mics are shifted forward of the gongs somewhat, so that the direct line to the gongs to those mics is more towards the backside of the cardioid pattern. The other thing is the dipolar radiation pattern of the gongs. Their direct sound will be much louder in front and behind than along the plane directly to the sides, above and below. So placing the mics in the same plane as the gongs is sort of like taking the "bowls sound quiet and thinner when mic'd from above" observation and using that to advantage as a way to intentionally pick up less direct radiation from the gongs. You'll still get plenty of gong sound, maybe too much. They won't radiate entirely and cleanly as a textbook dipole, plus there will be plenty of diffuse gong sound bouncing around the room which will be picked up regardless of where the mics are or which direction they point. This will take some experimentation to get a feel for the appropriate position relationship between the gongs and the mics.
I'd still combine that with the X/Y mic out in front, facing toward you across the top of the bowls in the center. I think the combination of a wide mic pair and the coincident center X/Y pair provides lots of mixing flexibility along with combining the best of both methods- the sharp imaging of the X/Y from a front center audience perspective, and the big open ambience and depth of the spaced pair. In a way, you are placing yourself and the array of bowls within a very close, inward-pointing decca-tree triangle, using all cardioid mics and an X/Y pair at the apex. Yeah, that's a bit of a reach, but I can see the continuum from classic Decca Tree to this.
Thinking about it, I like this idea for some other reasons too, somewhat related to the recording I do with my oddball surround recording setups. The X/Y mic is in front facing away from the audience and at you. The wide-spaced cardioids are in back pointing out into the room and facing the audience. The bowls on either side are closest to the wide-spaced cardioids (arranged as necessary for best balance and playability) so the bowls will be the most up-front and present sounding things in those hard-panned Left/Right channels, and pickup of the audience and room sound will be reproduced widely and diffusely from the Left and Right speakers. The X/Y mic is facing away from the audience so the center of the image isn't cluttered with audience and room ambience but focused primarily on the bowls across the center of your arc in front of you, your speaking, singing and flute playing. The entire bowl and gong array is picked up with X/Y stereo cues as well as spaced time of arrival cues, and the gongs are far enough away to not overpower the X/Y channels. The three mic positions should get decent coverage of all sources with good proximity to everything, and the phase/time-of-arrival between the three positions should be sufficient for capturing good sounding modal phase stuff, while being different enough and limited in number so as not cause a comb filtered mess.
Remember when mixing it that the mics are pointed in opposite directions. So think in terms of stage-left/stage-right rather than mic-left/mic-right when mixing the left cardioid with the left X/Y channel and vice versa.
This isn't actually that far from Bruce's suggestion, and if you were interested in trying to do this using only two microphones I think his suggestion is the best so far. This mostly just shifts those two spaced cardioids somewhat so they work better in combination with the center X/Y mic facing the other way.