One legged burnouts are killing my 1/4!

[chris91LX]

Went to the track to try for the elusive 13 second timeslip and found out I'm only spinning one of my wheels. Still ripped off a 1.97 60' time, but I'm thinking I need to get this taken care of in order to get into the 13's. My questions are:
1) Do I rebuild the Trac-Loc or go with an Auburn or Eaton or Detroit locker etc. (which would be best if I do?)
2) Should I replace the axles while I'm at it, I'm not made of money but I don't want to do this twice either.
3) Can I do this myself or do I need to have a mechanic do this, I'm good with tools but never worked on a rear end. Local shop gave me a price of $800-$900 for the auburn and labor.
Right now my plan is to eventually go low 12's on motor, maybe high 11's, so keep that in mind. Thanks in advance for any help.

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91 LX 5.0
Z t-5, 3:73 gear, Vortech 73mm Mass Air, Accufab 65mm TB, BBK underdrives, Crane HI-6S Ignition, BBK unequal length headers, Bassani x pipe, 2.5" Dynomax Super Turbo cat back, Kenny Brown Super Subs, Factory Five Control Arms, Mac cold air kit, Nitto D/R's and more to come!