Array of telescopes with single orbiting collector? Might such a thing give better images than we could get from other virtual telescopes with multiple collectors? Or is having multiple collectors not a limiting factor? Could a single collector compensate for atmospheric distortion in a way multiple collectors cannot?

We sometimes use arrays of radio telescopes spread over a wide distance to increase the effective aperture. I think that array is called a virtual telescope, but I might be wrong. A normal radio telescope has a collector in the same way that a satellite dish has a collector. The reflector of a radio telescope is parabolic so as to focus parallel waves to a single point. That works because dish and collector are in a fixed geometry. The reflectors of my imagined telescope would need to turn so that they reflected waves from whichever part of the sky was being observed onto the collector. That turning would change the required curvature for perfect parabolic-ness. 

The telescope I'm imaging would have a (perhaps geostationary) satellite as the collector and an array of flat-ish reflectors spread over hundreds of kilometers working together to collect waves from the same part of the sky. Being non-parabolic, the reflectors wouldn't be very efficient, but they could compensate by being numerous.

The collector wouldn't have to be geostationary, because the reflectors already need to compensate for the earth turning; adding the satellite's movement into the equation wouldn't be terribly complicated.
If I understand your question, what you're talking about is one of the things that has been on the astronomical wish list for ever.  There are two ways to combine separated telescopes.  One of them (the easy way) is to just overlay the images from the two telescopes.  In this way you get to double the light you collect, but you have to take care to overlay the two images very well, such that they have the same magnification, rotation, etc.  The resolution you get doing it this way is only the resolution you get from either individual telescope, so the main reason for doing this is to increase you signal-to-noise (it doesn't make sense to do this if you're looking at a bright scene).

The other way to combine multiple telescopes, which is along the lines of what you are thinking, is to phase the two telescopes, meaning that not only are you laying the images on top of each other, you are also doing it so that the two images have the same phase, meaning they have traveled exactly the same distance from source to collector.  What you gain by doing this is that the resolution you get this way is what you would get if you had a telescope aperture that circumscribed the two telescopes.  For instance, if you had two 10 cm telescopes separated by 10 meters, you'd end up with an image that had a resolution of a 10 meter diameter telescope; however it would only have the light collection capability of the two individual telescopes, so though you have the resolution of a 10 meter telescope, you have the light collection capability that is only $\frac{2*{0.05}^2}{5^2} = 0.02\%$, meaning that you'd need to take an exposure of 5000 seconds to get the same signal you'd get with a 1-second exposure with a 10 meter telescope.

The reason you can easily make these virtual telescopes with radio telescopes is that the level you need to match path length goes as a fraction of the wavelength you're looking in.  Radio waves are many many meters long, so if you need to match the path length to, say, 1/50th of that, you're talking distances that are on the order of many centimeters or even meters.  What this means is that the radio telescopes can measure the incoming radio waves and time-tag them with atomic clocks; the ability to time-tag and the level that we can synchronize separate clocks results in phasing errors that easily fit within the phasing requirements.  Radio astronomers can record the data at each telescope then after the fact combine their signals in a computer.  However, for visible light, a fraction of a wavelength is now on the order of nanometers.  We currently don't have the ability to time-tag optical data to be able to go back later and do the phasing, which means the phasing has to be done real-time.

So the challenge to do what you are suggesting is that we need to phase the separate telescopes in real-time.  This means that we need to hold the optics in the separate telescopes so that they are not only matched to the nanometer level, but you need to hold them to that level as you are imaging.  We can easily do that on an optics table in the lab, which is basically what you are doing when you make a Michelson interferometer, but doing it on separated satellites that are moving around, vibrating, etc., it is a bear of a challenge.