That sucks about your rear axle... I'd say your best route now is to find a full floater 14 bolt. Quite a few will have 4.10 gears, or if you can find a military 14 bolt then it will have 4.56 gears with a detroit locker.
Your 3.73 gears wouldn't have been a good match for you new larger tires (whatever size you are going to run).
Yes, driveshaft length will be different, but they needed to be modified anyway for your 6" lift.
A detroit isn't the smoothest easiest thing do daily drive- in winter it can fish tail around corners. I've gotten used to it and daily drove mine for a lot of years.
Detroits are probably the cheapest option, but if you want 100% smooth and don't even know it is there then get an Eaton Truetrac. I have one in the front axle, and talked my buddy into putting one into the rear of his Silverado. He loves it.