Does anybody know if it would be possible or if anybody has ever tried to put a 2003 powerstroke engine and 6-speed transmission into a 1997 F-350 Powerstroke?

 

Sure, it's possible.
You're talking ALOT of money though, why would you want to do it.
The right shop could put a 7.3 in a Pinto if you got the bucks.

 

Now there is a scary picture
Checkout www.fordcummins.com they do cummin's to Ford truck conversions. They are going to be doing them for chevy and the small 4cyl cummins in Jeeps.

 

Well, the motors are already basically the same, different turbo, and an intercooler, are the "major" differences.

There are a couple of guys that have swapped out the Zf 5speed to the Zf 6 speed, and basically need to change where it mates to the motor, I remember one guy who put a 6 speed in an older IDI truck, and it worked fine.