Well, this thread certainly piqued my interest...so much so that I spent about the last 4 hours reading about aerobic acetobacter fermentation.
I have a background in environmental bioremediation, so i'm familiar with these processes to a certain extent.
That being said, I fear that your recipe will not yield the desired result. "Bugs," as we call them, do some magical things, so i wouldn't write the experiment off just yet. I will say however that acetic acid producing bacteria tend to thrive in an aerobic aqueous environment with a pH between about 5 and 7. Like all organisms, their growth rates will be impacted by swimming in too much of their own "shit."
Vinegars, as you well know, start with a solution of sugars and water. The sugar is converted into ethanol by yeast, and the ethanol is then oxidized by bacteria to yield acetic acid. The "scoby" in kombucha is actually a symbiotic mass of yeast and bacteria, and can actually be used as a "mother" for sugary vinegar feedstocks.
The reason i'm skeptical about the above recipe is that lime juice has such a low pH that ethanol synthesis is unlikely to occur via the action of yeast. With no ethanol, there can be no acetic acid by way of "mother."
A suggested workaround (should the above method fail) would be to dillute the lime juice with a simple syrup. This would provide a better feedstock for the yeast during the anaerobic phase, while also raising the pH to a more acceptible level.
As an aside, after reading this thread, I decided to try to make cognac vinegar.
solution A (6% ethanol by volume) is composed of the following:
100mL 80 proof cognac
550mL distilled water
16 mL Braggs unpasteurized unfiltered vinegar "with mother"
solution B (6% ethanol by volume) is composed of the following:
100mL 80 proof cognac
560mL distilled water
10mL kombucha "scoby"
</two cents>
here are some links that might be helpful:
http://ohioline.osu.edu/hyg-fact/5000/pdf/5346.pdf - Ohio State University Extension - "making cider vinegar at home"
http://chemistry.about.com/od/foodscienceprojects/a/How-To-Make-Homemade-Vinegar.htm -
Anne Marie Helmenstine, Ph.D.
http://en.wikipedia.org/wiki/Acetic_acid_bacteria
also i should add that my cognac experiment will be held at a temperature of 80F, in glass vessels, and shaken once weekly to increase DO (dissolved oxygen concentration).
-Matt