I don't think for your app you really need a break in because you kept the gears, for others taht swapped the gears, I think the following would apply.

Follow the break-in procedure religiously for the first 500 miles. The idea is to allow the gears to set into each other and slowly them harden. The first 30 miles of heat cycles are critical for proper break-in - nice and easy. For those first 500 miles try to not drive for more than 30 minutes without letting it sit for 30-45 minutes.

Andrew

 

Gears need to be broken in/heat cycled...Eaton doesn't.
If the gears area already used, have at it

If they are new, don't drive more than 15 minutes at a time or abouve 55MPH for the first 100 miles. The next 250 or so miles you can drive for longer periods of time, but still don't go above 55MPH, and let the differential totally cool down. At 500 miles change the gear oil, if you have the Eaton make sure you add the recommended GM oil and GM friction modifyer. When I got my Eaton it had the GM factory part numbers for the oil and additive.