Has anyone any experience with taking a typical 2-seam fastball grip and moving the index finger over to the middle finger and throwing it the same as the fastball?
Not sure what you call it other than a variation of the slider, or 2-seam slider?
Anyone have any experience with this particular grip?
The ball movement from a right handed pitcher is down and to the left with the ball rotating sideways.
It’s called a “cutter”. The other way is a sinker.
I guess I’ve only seen 4 seam cutters, and when you say the other way, you mean outside the narrow part of the seams as opposed to inside?
I don’t think that it makes much difference how one grips the ball. When I was learning the pitch, my coach—an active major league pitcher who threw a very good one—demonstrated the grip, which was very much off-center, with the index and middle fingers very close together and the middle finger just touching one seam. The key is the wrist action; he told me, “Throw it like a curve, but roll your wrist, don’t snap it.” I threw my curve with a karate-chop wrist snap, so he told me to simply ease up on it. He demonstrated this, then handed me the ball and told me, “Go ahead—try it.” I got the hang of it in about ten minutes, but it took me some nine or ten months to really get that pitch down cold, which was what I did.
I was, by the way, a natural sidearmer, and I was using the crossfire a good deal—in fact, I fell so in love with that delivery that I used it with just about everything I threw! I found that it gave me twice as many pitches as I had in my rapidly expanding arsenal, and the batters used to have conniption fits right and left because they couldn’t hit it to save themselves.—My coach showed me how I could change up on that pitch, always being sure to throw everything with the same arm speed and the same arm action. 
8)
My son throws throws a 2 seam close to what you describe.Either he positions his index and middle fingers along the inside of each of the seams, or will move his index finger alongside of his middle finger and throw it like a fastball. The tighter the spin he puts on it influences the break.It’s a lateral break starting in on a RH batter and having enough movement to catch the outside corner or get the hitter to hit it off the end of the bat. Or sometimes if it’s too much it will break outside.
[quote]I guess I’ve only seen 4 seam cutters, and when you say the other way, you mean outside the narrow part of the seams as opposed to inside?
[/quote]
Classic two seam over balance…One way sinks the other way cuts…4 seamer can naturally sink too.
I am 100% sure that is a cutter, partly because I throw one, and partly because of this article: http://www.thecompletepitcher.com/how_to_throw_cutter.htm
“This gives you a pitch somewhere between a fastball and a slider, and, thrown properly, that’s how the pitch will move, like a very tight slider.”
That is what Steven Ellis says in the article.