Patience...
Not to deviate from the tire discussion, but...
Patience is your friend, especially on a budget. I've been spending a lot of time seeking "free" or "almost free" upgrades lately, with some success. I've picked up a 22 ft travel trailer (free), an 8 foot pop-up (75 USD), sunbrella canvas to repair the pop-up (5 USD), two fiberglass truck caps (one free, one 60 USD), set of four stock rims and tires with 1/2 tread (50 USD)... all in the last 3 months or so.
Point is... keep your eyes open and ear to the ground, and parts will come to you. If you want a gear change and locker/LSD, shop for a truck with one and swap the whole rear, then sell the donor truck (done that, too.) I agree with the 3.73 gears, easy to source in a stock truck to swap, and a good match with 31 or 32 inch tires. My K5 had 33-12.50-15 and 3.73 with a 700R4, and got 14-15MPG reliably.
IMHO, nothing "wrong" with the rims you have, pick up/find some salvage yard tires and try them out. 31-10.50-15 tires are a dime a dozen around here, and may be worth a try.
Good luck with the build.
:campfire:
On edit... I see now you have $ for tires set aside. Would it be worth it to "try out" salvage tires for cheap first, run them for a while to see how they work for you, and then buy the new ones later? A least you would not have to tolorate a potential "mistake" for the life of the new tires. Also, Yokohama tire has a 30-day money back guarantee. Not sure of the details, but this may be an option if you can get them near home. The Geolandar A/T + 2 may be my next "new" tire.