Changing the rear end fluid isn't a bad job and adding the limited slip fluid won't hurt if it doesn't have it. I used a Mobile product for limited slip. I have no tag but the wheels turn opposite each other. Changing this fluid in my Benz after 20 years yielded the stinkiest fluid I ever smelled. My wife even made a comment. I changed it in my BMW but it smelled fine. I think it was already changed in the BMW.

Regarding buying a new car, I would only do it if I intend to stop all my DIY work. The new cars are "black boxes" and lots of the repairs are designed to make you buy a new car. Look at exhaust, cats and sensors. At a mechanic's shop I saw a rusted out exhaust off a newer SUV and it was $2500 with no way to repair. A mechanic friend told me when he went to work at his first job (GM Dealer) that his job is to sell new cars. Find so much repair that the customer wants to buy a new one rather than spend so much to repair the old one. Most cars today, even super expensive ones are disposable. Can you imagine an engine rebuild on any AMG Motor?

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Steve
1985 Mercedes 500SL Euro (Gray market)
1995 BMW 520i Euro (Gray market)
1992 BMW 525it Wagon
1994 Honda Del Sol Si