Yes, you are on a fool's errand, but you might learn some new ideas while you are on it.
Why not consider a 4-string tenor guitar? Those are tuned in 5ths like a banjo. The lowest pitch on the tenor guitar is the C above the E on the regular guitar. But there is an alternate tuning for the tenor guitar where the lowest pitch is the G above the low E on the guitar, or a minor third higher. In the G tuning, the tenor guitar is tuned like a violin, but one octave lower.
You are aware of course of the issue that the mandolin is tuned in 5ths and the guitar is tuned in 4ths--I hope you are taking that into account.
There are a number of "baby" acoustic guitars on the market now which have the shortest possible scale length that can still accommodate standard guitar tuning.
- A mandolin has a scale length of 356mm or 14 inches.
- A standard acoustic guitar has a scale length of 648mm or 25.5 inches.
- A "baby" guitar has a scale length of 584mm (23 inches) or 559mm (22 inches).
Any shorter than 559mm and you can't adequately produce the low "E" of a guitar.
Some "Baby" guitars of good quality:
Be sure to check out specialty instruments by Gold Tone. They make some freaky cross-over hybrids between mandolins, guitars, basses, banjos--you'll just have to see the site and view the demos!
Gold Tone has a new mandolin with a 6-string guitar neck on it, tuned in 4ths, but of course it plays the range of the conventional mandolin. It does not go down to the lower octave of a real guitar. I played one of these at the Summer NAMM convention in Nashville last month. It's an impressive instrument, but it's not quite what you are looking for.
Then there are the octave mandolin, the Greek bouzouki, and the banjo, all of which do in fact go down close to the range of the guitar (and lower than the mandola), yet are tuned in 5ths, not 4ths.
Finally, as a left-field choice, if you want a real acoustic guitar, tuned like one, but you want the thinnest, narrowest neck, you might want to consider the Daisy Rock Girl Guitar brand. They are quite hideous in aspect but they are designed to be played by, well, girls, with small adolescent hands. Nothing wrong with that, mind you, but a sparkly pink guitar may not be your thing.