Re: How about an NS Guitar?
You're in luck. Turns out that the 7 and 8 string strat-like guitars so popular with shredder types are widely available from companies like Schector, ESP and I believe Charvel as well as myriads of custom shop offerings. Here's a well made and really quite inexpensive 25.5" scale 8 string from ESP and for $500 you could find out if the concept works for you:
http://www.sweetwater.com/store/detail/ ... oCMJPw_wcBI had 2 different 7-string guitars during my guitar career - one Guild jazz box in 1980 and one of these shredders - a Schector in the mid 90s. Both fine instruments and both w/an added low B string. I had other guitars I played more often and I was faced with the difficulty of going back and forth between 6 and 7 strings. It was gonna have to be one or the other and practicality won out in the end. Plus in a band, the occasional penetration of the low string into the bass players territory created a few issues and 8 strings could be worse. Solo though it's a fantastic addition. I saw some old school bebop guy at the NAMM show a few years ago with an 8 string Tele looking thing and he was exploiting the hell out of that concept in a most brilliant fashion although he wasn't a tapper. He just used the extra strings to add range to a given position.
Or - you could just put an extended guitar tuning on an NS. (I think Emmett offers that) You got a longer scale (34") and you can cop all the playing styles you mentioned. That's by far though the best way to go to achieve your criteria in my opinion. Of course the only thing you gain over a full blown Stick tho is the ease of fingerpicking so pick yer poison.