The idea of a turbo single AA perplexes me greatly. Firstly, turbo suggests that you would like to be able to throw light a good distance, and want a larger light to house a larger reflector. AA suggests you don't mind the tradeoff of having lower power for a larger, less energy dense light with higher "convenience" factor. Single cell suggests you'd rather have a small light than a larger, more powerful light.
So you are asking for a small (and large?), low-powered, long throw light?
I would suggest removing one of your criteria to make your list less of an oxymoron.
For instance, losing the AA requirement gets you a twice powerful light, since 123 is twice the voltage and affords more power to the LED. That'll give you what, twice the throw in a similar (smaller) package?
Or, losing the single cell requirement gets you some pretty intense stuff. For just one more cell, you could have a Quark AA Turbo (if you lose two requirements, you could get the 123 Turbo, even better!) which is essentially what you're looking for anyway. Or, you can go for Or, you can go for two more cells than that and get the best throwing AA light on the market... the
DEFT FTP. Quite affordable too, actually...