I don't think this will work for 31's BUT
This was my solution to gearing my 4-dr which came stock with 5.125:1's
Kick T-case High range is 1:1  Add an OTT adapter and marry a sammy caseÂÂ

Stock sammy t-case high range is 1.409
5.125 (axle ratio)      (multiplication factor of sammy High range reduction)
x .409
----------------------
2.096125 ÂÂ
2.096125
+5.125
========
7.221125
7.22:1 High range rear axle ratio is GoodÂÂ
Izook gear calculator says if your tire is 27" and you switch to 36" then you need a 6.833333333333333 axle gear to get back to the stock ratio.  Hope the extra .4 will help with rolling resistance ect...  Now how do you fit 36's under a kick again?
I got lucky and found a deal on mine used. It came with the everything you see here and was used under a sammy on 37's for 2 runs.  Web site is OTTindustries.com

