It will be MUCH easier to pull the center section and do the work on a bench.
You will definately want to get a MMC shaft BEFORE you do this (approx cost $450). You will thank me when you can cruise at 80mph without a horrible driveline vibration.
You will need (not a complete list):
36MM axle nut impact socket (to get the halfshaft nut off)
Torx bit (TX500) to get off the lower cont arm bolts
Dial indicator with base (to set/check backlash and ring gear runout)
Large 2 or 3 jaw puller to get Knuckle off of cv halfshaft
impact gun with assortment of sockets
21mm deep to get off forward center section mounting bolts
RTV to seal up the center section cover
Torque wrench good up to 110FT*LB
Diff rebuild kit (shims, bearings, end seals, the works)
New 36mm axle nut (may have to mail order)
VSS sensor for 4.10 gears (goes into tranny)
You really should get a mail order SCT tune in conjunction with this mod
You should have a good protractor to check the pinion angle afterwards.
I'm not trying to scare you but this is a big deal. I have done this twice on Marks (last time was last month). I remove the center section in one session (about 3 hours), rebuild the diff the next day (minimum of 4 hours to get right you first time - could take 12+). You need to get a nice pattern, the right backlash, and the right carrier bearing preload. The third day do the reinstall and tie up loose ends.
You will likely find other problems while doing all this. Last time I found a leaky brake hose on one caliper and both sway bar end links were shot. Also - my pinion angle was off and required shims.
Where are you located? It would be good to have someone who has done this on a Mark help you with the R&R, and then have help from a rear end specialist for the actual rebuild/gear swap.