Technique recommendation for this line

[xiolo]

G:-4-4---9-9---12-12-9----4-4--9-9---12-12-12---------|
D:-------------------------------------------------------|
A:-------------------------------------------------------|
E:-3-3---8-8---12-12-10----3-3--8-8---12-12-12--------|

G:-14-14--9-9--12-12--11-11----4-4--9-9---12-12-11----|
D:-------------------------------------------------------|
A:-------------------------------------------------------|
E:-13-13--8-8--12-12--10-10----3-3--8-8---12-12-10----|

This is the line I'm playing. It is from Trading My Sorrows (christian worship song) http://www.youtube.com/watch?v=mXi5iq1zAl4

Right hand is straight forward, plucking with my thumb and middle finger.

I'm having some trouble with my left hand. I'm trying to play the whole line with my 1st and 3rd fingers, but it gets really tough playing the 12th fret and higher. I'm playing a 5-string Ibanez SR505, and am thinking it might be a little easier with a wider spaced 4 string, but I don't have one. I've adjusted the height so I'm playing with it at the same height I would when I'm sitting down which also seems to help a bit. Would you guys play it with the same fingers, or switch it up to fingers 1 and 2 for the high stuff and back when it is lower? (cumbersome I find, but doable with practice I guess)
Also, what would be a good way to get rid of the resonance of the notes on the middle 2 strings? I can't seem to mute them properly, but then I'm new to this whole double stop style of playing. It just sounds so good.

Any tips would be greatly appreciated.

[JWClark(ABD)]

I just read through it and played it w/ 2 (on the E) and 4 (on the G). This frees up 1 to mute the middle strings. The 2&4 fingering is my default for laying 10ths, and usually it works out. Was the 9th at the end of the first phrase (3/4, 8/9, 12/12, 10/9) a typo or intentional?

[xiolo]

Oops. typp it's supposed to be 10/11, not 10/9.

So you use your middle and pinky(2 and 4) fingers and your ring(3) finger to touch the middle strings to keep the sympatheic resonance down?

[Dogbertday]

I would use 1 on the E and 2 on the G when the note is on the same fret(m10th) and 3 when the note is up one(M10th). This way your first and second fingers act like a movable capo for those two strings and you just have to lay down your 3rd finger as needed

[xiolo]

Originally Posted by Dogbertday

I would use 1 on the E and 2 on the G when the note is on the same fret(m10th) and 3 when the note is up one(M10th). This way your first and second fingers act like a movable capo for those two strings and you just have to lay down your 3rd finger as needed

I'm sitting here moving my fingers through the air trying your recommendation out. I think my co-workers think I'm a little nuts. I'll have to try that when I get home and have a bass handy.