Most of the aftermarket differentials I have installed never seem to be able to use the same shims that had the backlash correct on the previous differential. Even if the original shims were to fit with the new differential, my backlash would be way out and the gear contact patterns showed the expected shift in contact. Bad pattern = noisey gears.
If you don't have access to any factory diff shims, Ratech makes an install kit for most rearend models out there that comes with bearings, shims, seals, etc. The diff shims in the kit are designed to be stackable. To make things easy, grab your calipers or 0-1" mic and measure and label the shims in the kit according to thickness. This will save you gobs of time when you are switching shims back and forth to get backlash in spec. In this diff shim assortment, you will find 4 of the shims to be .100". These thick shims are meant to sandwich a combination of thin shims between them to stack up to your desired thickness to go behind each diff bearing cup.
What I do first is to come up with a shim thickness on each side to where I get an easy but snug fit of sliding the diff assy between them. Check backlash and make adjustments by removing x-amount of thickness from one stack and adding the same x-amount to the other side to keep your snug fit. Good thing about most aftermarket gear sets, the desired backlash dimension is usually scribed onto the OD of the ring gear somewhere. Once you are satisfied with your backlash dimension, do a gear pattern check. You may have to do some tweaking on your pinion depth shim and/or backlash setting to get a good pattern. Most of the time if you go by the dimensions scribed on the gearset, you won't have much adjusting to do, if at all. Then add .004" of thickness to each side to put some preload on your fresh diff bearings and reinstall for good.
Where a headscratcher comes in is if you have a lot of bracing welded to your housing. The distortion from welding tends to disturb the original pinion centerline to diff centerline relationship. If you rely solely on the numbers scribed on your new gearset without doing a pattern check, you usually end up with noisey gears. When dealing with a reinforced housing, the right numbers are touch and go depending on what you get for a contact pattern. Sometimes you will assmeble and reassemble the damn thing 8-10 times in your search to get a good pattern. At least a good pattern = quiet gears.
You 9" guys are lucky, you can reinforce your housing all you want and your gears never move due to the removeable hoghead design. Why Ford quit making the 9" is beyond me.
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