I recently built what you are describing by putting a Warmoth baritone conversion neck on a Squier VM Jazzmaster. The lowest I could seem to tune it was to A-D-G-C-E-A. I used the lighter 5 strings from a set of Bass VI strings, and an unwound .020 for the high(er) A string. A fun baritone, but not what I would call a bass.
The extra length of inactive string behind the bridge on JM style guitars helps with the tension issues when tuning that low, but in the end, if you want a true Bass VI (tuned to low E), I would say just have 'em build ya what you want. JM pickups' voicings don't lend themselves to the lower tuning, IMO, (I later installed some CiJ JM pickups that weren't as thick so I could get something like clarity), and I found it desirable to install a buzz-stop on the tail piece with the larger gauge strings.
I would think that Warmoth has designed the Bass VI to perform well with the heavier strings and lower tuning, and so if you have the $$$ for made-to-order, I would go that route. I tried to put VI strings on a baritone only to find out that the old saying is true: "Sticking feathers up one's butt does not make them a chicken".
