I went from 3.73 to 4.181 and it was probably one of the best changes I've made aside from the turbo swap. It was my first time doing any gear work and I was able to figure it out so I bet you will be able to as well.
Easiest way IMO is to:
- Buy the whole 3.9 carrier assembly from a donor car (lots of them on ebay, just verify what you are ordering so you get the correct gearing)
- Then take the LSD out of your current carrier
- Attach the 3.9 ring gear to you LSD
- Check backlash and pinion gear depth - I used the spacers that were in my car paired with the LSD, but this might not work for you.
- Take your LSD with the 3.9 ring gear attached and install it into the donor car carrier assembly
- Turn it by hand to make sure its moving freely before you reinstall it.
For me it was a direct bolt in to put my LSD in a 4.181 carrier, I didn't have to adjust pinion depth or backlash, but you might have to play with the shims and if you do it can get a bit tedious to get it right. After I installed it I filled it with new gear oil and ran it easy for 500 miles, then changed the oil again. I ran it for the summer and changed the oil one last time before putting it away for the season. I only did this to help ensure the gears meshed correctly and then clean out any metal particles that resulted from that process.