In terms of "oddball" for non-surround recording, I'd really like to try out the Omni+8 setup.
That setup has interested me and in other threads at TS I've suggested tapers give it a try in certain situations. It's a variation on spaced omnis + center mic, which is the starting point of most of my oddball techniques.
I think it's applicable to TS partly because it is relatively simple, using just 3 channels. In terms of 2-channel stereo, I see it as a variant on the classic Decca tree 3-omni triangle approach. The advantage I see in using a bidirectional center mic rather than some other pattern is maximally increased forward directivity of pickup in the center (an ever-increasing incremental change moving from center-omni > center-cardioid > center-supercard > center-bidirectional). In some ways it's similar to using a shotgun mic in the center in that sense.
Several basic aspects in play here:
1) A bi-directional achieves the most-narrow angle of forward sensitivity achievable in the center mic (other than a multi-capsule DSP shotgun like the Schoeps CMIT), along with a very smooth and well behaved polar pattern. A typical shotgun may be similarly forward directional, or perhaps even more so at high frequencies, but it's polar-pattern varies far more with frequency and is typically quite ragged. Combination with the omnis covers that raggedness to a significant extent in contrast to a shotgun or pair of them alone, but it helps if all three mics share the same timbre for best tonal blend and image stability. A bi-directional is more likely to be of the same timbre as the omnis (above several hundred Hz) than a shotgun and blend more smoothly in a mix.
2) As a great practical setup advantage, the increased degree of forward directivity allows for a less wide L/R omni spacing without introducing to much inter-channel crosstalk which would otherwise compromise image width and make things overly monophonic. Remember, if you are using any kind of center mic at all, you'll want the R/L mics spaced wider (or angled further apart, or both) than you would if using just the two microphones alone. If I'm using 3 omnis instead of 2, I generally want to double the L/R spacing. A more directional center mic allows for somewhat less wide L/R spacing. A bi-directional or shotgun center is the logical conclusion of that trend, allowing for a more reasonable spacing of the omni pair, more easily achievable on a single mic stand.
3) The bi-directional pattern has the least sensitivity to the immediate surroundings beneath the microphone in the immediate vicinity around the mic stand. It does have equal sensitivity to the front and rear, but if up say 9 or 10' on the stand, the most proximate audience nearby (and thus the loudest by proximity) is in or near that null.
4) I like arrays which include a rear facing microphone (when recording four or more channels). Just a bit of that rear facing channel mixed in makes the recorded ambience sound far more natural to me. Obviously how much can be used depends on the sound of the venue and the behavior of the audience behind the recording position, but Rocksuitcase has confirmed to me the value of a rear facing mic in his experiments as a well. A center mic pattern with some "rear lobe" achieves that without a 4th microphone, if in a less controlled way. In a good room with a good audience, a bidirectional center could provide a perfect balance in that regard. Consider that the omni + 8 is equally sensitive to the front and rear. In that aspect if not others it is similar to Blumlein or a pair of spaced omnis. Yet it will have more front/back reach than a pair of omnis or Blumlein with less sensitivity to the sides, above, and below. In most cases I expect using a hyper-card or supercard in the center will be preferable, providing greater forward sensitivity bias with with less sensitivity to the rear, but still enough to help with this ambient naturalness in comparison to a center shotgun.