Yes, Carp Happened! But in the end, you accomplished what 99% of automobooble jockies wouldn't even try...
You on the other hand, have proven that yes, in a pinch I CAN DO THAT!
I don't know what experience you have with mechanics, but you did a great job,
Saved yourself a differential full of bucks (To be applied to additional goodies) & next time,
it will be a piece of cake!

I applaud your well produced journey & it's outcome!