When installing a taller tire it makes the gear ratio higher requiring more power to turn the rubber. Your crawl speed will be faster and your on road performance will decrease. The best fix is installing lower gears. The lower the gear ratio the numerical translation will be higher such as 4.27/1. The higher the gear ratio the numerical translation will be lower such as 3.07/1.
Your ring and pinion gears are designed to run with precise tolerances.
Any gear misalignment or deflection can cause noise, premature wear and failure. So take your time!

The Pinion Gear is driven by the driveline.
The Ring Gear is driven by the pinion gear and bolts to the carrier.
The carrier holds the ring gear and the the unit that turns the axles such as the spider gears, locker, posi, spool, and of course the well known Lincoln Locker named after the welder that most use for welding the spider gears together.
Lincoln Lockers are not recomended.

Make sure to mark the carrier bearing caps so that they are installed in the same position as they were taken off. Also record the amount of shims that were removed for reassembly. Make sure that all parts are clean and all seal surfaces are polished with emery cloth.

Use gear oil on all parts during assembly.Install the pinion with the old shim thickness and no crush sleeve. Tighten the pinion shaft nut till you obtain proper pinion bearing preload measure with an inch pound torque wrench. You are measuring how much torque it takes to turn the pinion shaft.

Assemble the carrier snug in the housing during initial assembly. For ease of removal and install. Use the old shims for the first assembly. TORQUE BEARING CAPS TO SPEC..
Use gear marking compound to chech geartooth contact patterns.
(I prefer the yellow stuff)
Check pinion gear depth which is how deep the pinion gearteeth contact the ring gearteeth. Moving the pinion gear closer to the ring gear will make the contact deeper in the teeth (towards the flank). Moving the the pinion gear away from the ring gear will make the contact higher in the teeth (towards the face).
Proper pinion depth will not be established until backlash is established. Do not worry about the contact being center from heel to toe this can be close but probably never exact unless precise machining of the housing is done. Trying to establish perfect contact from heel to toe, you will usely end up with a noisie differential.

Check backlash with dial indicator. If the backlash is too much shim the ring gear closer to the pinion. If there is no backlash shim the ring gear away from the pinion gear. I like to set the backlash a little bit tighter than spec because after final assembly its usally a little looser than what you set it at.
After making final adjustments of gear contact patterns you need to install crush sleeve and and retighten pinion nut to proper pinion bearing preload. It Takes 300-400 ftlbs. to crush the crush sleeve. Air tools are a must. If you overtighten you must replace the crush sleeve. Tap on both ends of pinion shaft with hammer and recheck pinion bearing preload.
Setting carrier bearing preload is very simple,"Make it as tight as you can" without damaging the shims.
After final assembly recheck all specs and contact pattern before installing axles, diff cover, and new gear oil.

Large Prybar
Inch and foot pound torque wrenches
Dial Indicator
1/2in Impact Wrench
Basic Hand Tools

Randy's Ring and Pinion
Dana Shim Tip