As I mentioned in my earlier post, the best starting point for pinion position is to start with the same thickness shims pack as was originally there. If the pinion is hitting the carrier, the pinion shim pack thickness is too thick and the pinion is too far back in the housing. Remove shims from the inner pinion bearing cup so that the pinion can move out toward the U joint yoke.
To remove the carrier bearings, you need a diffrential side bearing puller such as this one by Snap On. Perhaps there is some place in your area that you can rent one from. A 2 Jaw puller and a bearing separator will also work.
As far as correct shimming of the carrier bearings, as I stated in my earlier post, it would be best to have setup bearings for the carrier. Shim the carrier so that you have no endplay (side play). Once you have established that, move shims from one side to the other until you have .007 to .008 backlash between the ring and pinion. Then torque your carrier bearing caps to spec, paint the gear teeth and take a pattern.
Do you have all the necessary tools such as Ft. Lb. and In. Lb. (dial or beam type for the In. Lb.) torque wrenches, dial indicator and micometers or dial calipers?