New Rear Diff, need recommendations...

Guys - I have a perfectly fine open diff at the moment, but will be swapping it out with a Detroit / Eaton TrueTrac. I wanted to get your advice and recommendations on a couple things.

I'm pretty decent with mechanical work. Pulling a diff is not something I've done before, but most everything I do, I've not done before. But I figure it out, take my time and usually do a good job. But on the diff, I've heard stories of guys not shimming them right (or something like that) and it screws the diff up in short order. If it's straight forward enough, I think I would like to do it myself, simply to learn. However, I have a guy I trust that does really good work himself. He is a mechanic and has a commercial shop, with a lift and all the right tools. He says he will do it for $150 labor. He also said he would let me help him on a Saturday (so I can learn). I'm thinking that's the way to go. Advice?​
The car has a 3 speed (727), 14" wheels/tires, and currently 3.55 gears. It is not loving the interstate. 3,000 rpm at 60 mph. I'm thinking about going back with the same 3.55 gears as well. Because my goal is to be able to cross the quarter mile in 13.99 seconds. With 3.55 gears, I would be trapping about 96 - 97 mph and turning about 4,800 - 4,850 rpm to meet that goal. That sounds like perfect rpms. With a 3.23, it would be turning about 4,400 rpm at 96 - 97 mph. I put priority on the 13.99 second quarter mile E.T., because ... I'm not planning on taking the Scamp on vacation! It won't see interstate runs very often. Not only that, but in the future, I may replace the 727 with a 4 speed. And then, it would be good to go for both the strip and the interstate. But I wanted to know your opinions. Do you guys think I could still hit a 13.99 with 3.23 gears?

7milesout