Which bearings did you replace?
I've got 4.56 gears and a Lock Right in my 35 and the drive shaft will turn by hand about 1/4-1/3 turn. As you go lower in gear there's less teeth on either the pinion gear or ring gear. When I had 3.73s and factory LSD my drive shaft would turn by hand <1/4 turn. The locker has it's own backlash in addition to the ring and pinion.
If you had a broken tooth on the pinion gear your Jeep would only go forward for about 8 feet at a time (give or take), coast for a bit, and go about 8 feet again as the pinion came back into contact with the ring gear.
Have you inspected the ring gear for any broken teeth?
By your description if you had an open diff I would say it sounds like a tooth is damaged/missing on one of the side gears. But with the Detroit you don't have the typical spider and side gear set-up. On dry pavement going straight with steady pressure on the gas you shouldn't be getting thrown around in the lane by the locker. Maybe a little sway in the back end when letting off and on the gas, but even that shouldn't be a violent movement.
How old is the locker? Could be a worn or broken spring behind one of the clutch assemblies or a spring that is somehow set up too tight in there.
Detroit Locker - Automatic Lockers - Locking Differentials
From the FAQ in the next link:
When I step on and off the gas pedal, I hear the unit make a “clunking” noise. Why?
Because Detroit Lockers have “backlash” or “slack” between the drive and driven teeth and you will hear this in everyday use going through corners and when going from drive mode to coast mode. Also with the vehicle on the ground and the transmission in neutral you will have 1\4 to 1\3rd of a turn of lash in the driveshaft, this is completely normal.
FAQ for Differentials
What weight gear oil are you using?
I'm using Valvoline 80w-90 right now to break in my new gears, but will be switching to Royal Purple 75W-140 (recommended weight for the lockers) here very soon to quiet down my Lock Rights. They're not loud at all, just want to try circumventing some of the pops and bangs I will sometimes get at low speed while turning in a parking lot. Perfectly normal for an auto locker to make such noises.