Thanks WWDiesel, [Edited heavily, please read again]
I thought of doing this for about 1 second, then abandoned the idea. It would mean buying more material, fabricating the new device. Instead, I noticed each of these case spreaders has only one point of purchase on the housing. So I just took one (the bottom) of my threaded rods out and readjusted a little. It worked fine. I was able to remove the spacers and measure them, one at a time.
Good luck is shining on me today. The two factory spacers were 0.005" different from each other, and located favorably to allow swapping sides. Switched the spacers from one side to the other and that made a little improvement. ...but not enough. When I wiggle the pinion gear, it still makes noise against the ring gear. Added a 0.003" shim and that helped more. The preload on the bearings is still within limits.
I'm taking a break to post my progress and express my excitement.
The kit has 17 shims ranging from 0.012" down to 0.003" There is (1) each 0.012". 0.011" shims, (2) each 0.010" shim, then (5) 0.006", (2) each 0.005", (1) 0.004", (5) 0.003" shims. I'll continue by replacing the 0.003" shim with a 0.006" shim. and check for backlash and preload again. If I can continue adding thicker shims I will, but I realize preload on the bearings will have a limit. I suspect that adding 0.006" will be the limit.
Measured the inch-pounds torque to rotate the ring gear assembly by using an open-end wrench socket on the 1/4" drive inch-pound torque wrench: 20-25 inch-pounds to break standing hysteresis, then free-wheeling after it gets moving. I'm a little concerned about that, but it is all dry right now. After a few thousand revolutions it may free-up.
This shows a socket on a ring gear bolt, but I'm turning the 3rd member with a 1/4" drive inch-pound torque wrench.
[Edit after a break] Added another 0.003" carrier bearing preload by replacing the .003" shim with the 0.006" shim. This tightened up the backlash clearance so this is only a tiny click heard by moving the pinion gear back & forth. I'm stopping there and calling it good for now. Certainly there are other noises coming from this 4X4 machine that will make the differential noise unimportant. Measured the clearance now to 0.006" movement on a tooth of the ring gear.
The third member assembly turns rather easily by hand, and driving it with the pinion shaft is very easy. Although I could not measure the pinion shaft turning with the 1/4" drive inch-pound torque wrench, I did compare holding a 14mm socket in my hand while turning it with the wrench. By hand I could only resist ~2 inch-pounds while holding the socket. The pinion shaft turns much easier than that, probably about 0.25 inch-pounds or less.
Dean.