The pattern is probably better with the .038 shim. If you can get the backlash to .010 it would move the drive pattern a little more to the heel and possibly make it look right. Increasing the backlash moves the pattern toward the heel. Closing the backlash moves the pattern toward the toe. Increasing the pinion shim moves the pattern toward the root and taking shim out of the pinion moves the pattern toward the face. Don't try to make up for backlash by changing the pinion depth.
If you can add some shim to the right side without taking anything out of the left side it might move the backlash .002. Do you have the shims tight enough that youc an not pull the differential out by hand? If you can't get the backlash to .010 then stay with .008 and .038 pinion shim.