tn,
Welcome to The NutzHouse!
In your request above, you refer more than once to overdriven pickups, particularly those that 'sing' when overdriven. I think you've confused the terminology here - pickups aren't driven, they drive other circuitry. That said, you have now introduced a very wide range of possible answers to your question, whether you knew it or not.
The fact is, to be overdriven, or achieve an 'overdriven' sound, the output of a pickup is what 'drives' a circuit out of linear operation, forcing it to distort the signal in some fashion, hopefully pleasingly so. You do correctly refer to pickups as being either high- or low-output, and that's proper terminology. And thus, higher output pickups will indeed force a circuit to distort more easily than a lower output pickup, that's simple to comprehend.
But where I have to scratch my head in trying to parse your request is this: you want a single coil sound to come out of a pickup that is sized like a humbucker - is that correct?
Err, isn't that what almost everyone else here is doing, in one fashion or another? Or am I being too quick to parse your request in terms with which I am familiar... I note that you don't refer, in your bolded sentence, to any switching. It would appear that you want to achieve a difference in tone merely by how strongly you strike the strings, thus how strongly you 'drive' the pickup. If that's the case, then it's easy to see why you chose to word your request as you did - it made sense to you, and now it does to me also, provided this is what you want.
But then you go on to ask if there are any 'trick' circuits that can arrive at this solution, and my head is back on its way to spinning 'round and 'round, wondering what you want. So. I'm gonna go out on a limb here, and pretend that you're asking if a humbucker-sized pickup can be made to sound like a single coil.
Short answer - no.
Better answer: not exactly, but close.
Detailed answer: The NutzHouse is full of threads/topics dealing with this very request, check around. Our Search function might give you what you want, or you can use Google to zero in on something more quickly.
As to other pickups, let me bring this to you: you can make a clear and clean sound into something dirty, but neither you nor anyone else on this planet can clean up a dirty sound. In this instance, an 'overdriven'* sound that starts out that way can never be brought to a state of sounding clear and clean - it just can't happen. So what you (seem) to want to do is start out clear and clean, and feed it to some circuitry that will dirty it up, in just the right tonality. That spells Kinman, right there.
I know, I know, there are probably 3 dozen pickup companies out there that can do the same thing, or at least they claim to. But when all the shouting has died down and everyone's gone back home, there's a reason Kinman charges more for his product - because it lives up to the hype. Pure and simple, if Chris Kinman says it's good, it is good, period. How do I know?
Because I've installed several sets of these things (mostly the Strat variety) into both hard-tail and Trem-O-Leo axes, and they always sound better than my own Strat, which has the SCn jobbies (originally designed for the Jeff Beck model, from the Custom Shop). That's a pretty tall hurdle to clear, as most players will tell you. Zero hum, crystal bell clarity, and yet they can sing the blues all night, come Hell or high water.
I would not hesitate to buy and install a Twangbucker, based on my experience with Kinman, no additional sound clips needed. But just to complete the process here, I must remind you that no matter what anyone tells you, a sound clip played on any computer, particularly those sourced over the Internet (especially YouTube!), will not be a true and faithful reproduction of the real thing. There are far too many limitations along the way, making even "side by side" comparisons a matter for ridicule.
You might ask around your local players' hangouts if anyone has tried Kinmans, or you might ask on the web, where you'll find both adherents and naysayers (no one has a 100 percent positive record, not even Kinman**). All I can recommend is that you listen to others with an open mind, some folks have personal agendas.
There ya go, I hope that helped.
sumgai
* Abusing terminology, I know, but it keeps the references in this topic on the same train of thought, without need for external translation.
** The reason some players "didn't like their Kinmans" was price. That was their business, sure, but I think they were cutting off their nose to spite their face. There's no pleasing some people, no matter how hard one tries.