I don't try to sound like Steve. But I would practice until you can't possibly practice anymore, then practice some more.
I would also try getting the Naked Tracks Set, and just jam out, don't try to be Steve, but just jam what your feeling, go with the flow, let your mind wonder. Then add some of those Vaiisms to your playing, the articulations, circular vibratos, type things. I'll admit it, I stole some stuff from my favorite guitarists
There is also a 10 Hour Workout written by Steve in a past Guitar World, It has some great insights on what he did to become what he is. Also the Guitar Center Masterclass on Steve's youtube channel has some insight into it.
As far as learning the songs, What I have to do is take 1 measure at a time, play it slowly, untill I can do it perfectly, (usually a very long process) Then move on to the next measure. I still strugle with most songs. I would start with Die to Live, It's been the easiest (by no means easy, for me anyways) but the easiest of the Vai tracks.