gratefulphish, you have the right idea. As you move your microphones farther away from the sound source(s) in a reverberant space, you will gradually pick up a greater and greater proportion of reverberation and a decreasing amount of direct sound. That will happen with any type or arrangement of microphones, though, since the sound field itself has different ratios of direct to reverberant energy at different distances.
You're also right that the apparent width of a sound source (or group of sound sources) decreases as you move farther away from it/them. Thus you don't generally need as wide a stereo recording angle (pickup angle) for more distant recording as you need for close-up recording.
However, there's a kind of paradox with microphone pairs, which is that the wider you angle your microphones apart, the narrower the pickup angle (the stereophonic recording angle which they can capture properly) of the pair becomes. So you don't want to reduce the angle between your microphones as you move farther from the sound source(s)--if anything, you may want to increase the angle between your microphones.
That's also why it is nearly always wrong to aim your microphones at the extreme left and right of the sound sources. The pickup angle of a given microphone arrangement never equals the angle between the microphones, other than by coincidence in a few special cases (Blumlein being the best-known one).
--intpseeker, as you may know, classic pressure transducers are essentially omnidirectional, while classic pressure-gradient transducers (velocity pickups) are bidirectional (= a "figure-8" pattern). But a microphone can combine some amount of the one type of response and some of the other, both at the same time, in its basic functioning. There's a mathematical way of expressing this using cosines, which I won't go into here unless someone really wants me to; anyway, a microphone manufacturer can mix the two operating principles in any desired proportion, and the result will be some directional pattern along a continuous spectrum that goes from omni through wide cardioid through cardioid through supercardioid and hypercardioid all the way to figure-8. (That's the spectrum of first-order patterns.)
One of the most interesting "vintage" microphones was the M 49, originally designed in the research laboratory of the German broadcasting organization NWDR and licensed to Neumann (Berlin) for manufacture. It featured a continuously variable polar pattern, along the spectrum that I just told you about. Most other variable-pattern microphones operate only at discrete stopping points along that spectrum, but imagine: If you could substitute a potentiometer for the pattern switch, you could create a setting that was exactly 73.88% pressure response plus 26.12% pressure-gradient response if you wanted to--and it would have a polar (directional) pattern to match that setting, based on the cosine formula that I just said I wouldn't bore you with.
Second-order patterns are mathematically and technically more complex; they involve multiple points of pickup which are combined with fancy circuitry and/or DSP. Very few practical microphones have ever been based on that approach, because it is so difficult for them to have uncolored response across a wide frequency range. The only commercial example I could come up with (in an earlier message today) used DSP, cost something like $3000 as I recall, and has been discontinued by its manufacturer after being introduced via a very interesting paper at an AES convention a few years ago. The remarkable thing about that microphone was that it held its very narrow pattern together across pretty much the entire range of speech frequencies, and that was quite an accomplishment for that type of design.
--"Wide cardioid" is a somewhat informal term; there really is no agreed-upon standard for that name or for its precise definition as a pattern. It really can be any pattern that anyone finds useful that's in between omni and cardioid; gratefulphish is right in implying that it need not be exactly in the middle, and with most manufacturers it isn't. One of the clearest ways to characterize a wide cardioid pattern is by the amount of attenuation it has at 180 degrees for a 1 kHz signal; generally this will fall into the range of 9 to 11 dB or so.
--best regards