RonK - sounds like the shims may have too much angle to them. What is the shim thickness on the "thin" end of the shim? I'm asking because the 3/8 inch thick at the center sounds like a lot.
Do you know the angle of the shim.
If I try and figure out the angle of the shim, here is what I have:
Assume the shim is 4 inches long.
Looking at the shim from the side, thin edge to the left, thick edge to the right. Half way along the shim at the center hole the shim is 3/8 inch thick (thats .375 inch), and the length from center hole to thin edge is 1/2 of 4 inches=2 inches.
Assuming the shim is very thin at the "thin" edge, and 3/8 thick at the center hole in the shim.
So the Tangent of the angle formed is .375/2=.1875
The inverse function of tangent is Arctangent. Solving for angle "theta" = arctangent .1875
Now go to internet, handy arctangent calculator:
http://www.rapidtables.com/calc/math/Arctan_Calculator.htm The answer is 10.6 degrees. This is WAY too much angle.
My assumptions may be wrong. If they are close, then you need much less angle, which would mean a thinner shim so you would not have to worry about the amount of leaf spring center bolt sticking out of top of leaf spring stack. Do some research to find what correct angle should be, although 2 degrees difference between driveshaft and pinion does not sound like too far off.
If the car is has an auto transmission, see if you can powerbrake it, and have a friend off to the side of the car and take a picture of driveshaft/pinion gear...is pinion now pointing parallel with driveshaft, or maybe pointing above the driveshaft?