Does a bathtub spout with a diverter have to be on the same side as the valve, or can I move it over to the side of the tub?
A normal tub diverter valve works because when the tub spout is open, it requires less force for the water to come out of the spout than it does for water to get pushed up to the shower head.  The water takes the path of least resistance.  When the tub spout diverter is closed, the water is naturally forced up the pipe to the shower head.

The reason the instructions say to only use one elbow and to limit the distance is to reduce the resistance of the water flowing out of the spout.  If the plumbing to the spout is too complex and provides too much resistance, you could have some water get pushed up to the shower head no matter what.

So, this plan might work, or there might just be too much resistance in the pipe snaking around the tub to the other side.  It's hard to say for sure.  If the valve is installed lower, I think you chances are better.  Also the tub spout pipe will have to go around the tub and not over it because water would certainly flow out of the head all the time if you did that.  Try to use only 3-4 fittings on the pipe - don't make any extra bends.

I looked around a little and found this forum post where a plumber used PEX pipe and three elbows even with the tub spout on the same side.  That was enough to make water dribble out of the shower head.  PEX could have made this problem worse because the fittings don't have a full 1/2" inside diameter so they restrict flow more than copper would.  Still, doesn't look good for your plan since you'd also have a minimum of 3 elbows (with PEX, 4 elbows using copper).