His Watchtower is mostly straightforward, aside from the break in the middle. Take a listen to Aerial Boundaries
or the mind-boggling Hot Type
. Once you see enough of his playing you'll see that Andy gets just about everything from him.
As far as style - they called him New Age
I think more because he recorded on the Windham Hill label than because of what he played. He called himself a "Heavy Metal acoustic guitarist" ;D .
A quote of his I always remember was: "I'm not trying to play the guitar, I'm trying to make music.", which reminded me of Zappa's: "I'm a composer who just happens to be able to operate this instrument called the guitar". Zappa was a big influence on Hedges, so the similarity in approach makes sense, even if the music doesn't show many similarities (other than Hedges covering Sofa #1
and My Guitar Wants to Kill Your Mama
I was experimenting with using flamenco techniques on electric in the mid-80s when Michael Hedges appeared and turned my head around. He incorporated some of the Flamenco percussive techniques with acoustic fingerstyle and threw in the electric players double handed tapping and extensive use of hammer-ons and snap-offs. Add a healthy dose of alternate tunings and he ended up with something unique.
But check out flamenco players like Paco De Lucia - the style incorporates a lot of percussive technique and interesting time signatures (they operate in 13 more often than not and the accents are really unusual for those of us raised on Rock and Pop) and is designed to be the solo instrument (although traditionally with dancers adding extra percussion - shoes and castanets).
Also check out Hedges' sometime bassist, Michael Manring, who often does solo bass shows in the same vein as Hedges. Fretless too.
Someone else I've been meaning to check out properly is Tuck Andress - I saw a song with him and his wife Patti and he was doing something similar in a Jazz vein to do bass, chords, melody and percussion simultaneously.