Right now I'm working on a particularly hard piece for my level of experience. I'm trying to learn "She is My Sin" by Nightwish. The part I have trouble with goes like this:

--------------------------------
5-----5-6-----6-5-----5-3---3--
--3-3-----3-6-----3-6-----1---1
--------------------------------

I'm not particularly adept with moving up and down the fretboard at a decent speed, and my fingers aren't stretched well enough yet to be able to use one finger per fret. So, seeing as there is no slides or anything, could I change it to this: (I realize my tabbing sucks.)

0-----0-1-----1-0------0--------
------------1--------1----3---3-
--3-3-----3--------3--------1---1
----------------------------------

....and get the same sound? It would make it much easier for me to play until I can stretch my fingers better across the fretboard.

It doesn't sound the same to use open strings, doesn't really matter but you will probably need to have a good dampening technique to avoid ringing tones.
If you play the same as you written then you will strecth your fingers on the same time as you practice it.

And you could play the bB on the 6th fret on e-string instead of the 1st fret on the a, and yo wouldn't even need to mave your hand.

But yeah, play it the way that suits you best.

I'm going to say struggle with it. Practice those bigger stretches and swift movements up and down the board - it will make you better.