I too own a 1983 Buick LeSabre original 307 engine with 202k miles on it. I've owned it since 06' (165k) and had the trans rebuilt at around 180k miles. She runs like a charm with minor problems that come with age.
I recently had the starter replaced at 195k, and I plan on replacing the carb soon. All in all, I'm very pleased with the car that only cost me $1100 four years ago.
OK, not that these aren't good cars, but let me tell you, you will not be burning much rubber, or hitting 130 MPH. Maybe you could burn rubber if your tires are bald, the road is wet, and you pour oil on them.
I've owned a 1978 Le Sabre with a Buick 350, and a 1981, 1983, and presently own a 1985 with the 307 V8. The 307 engine is durable, but not powerful. It struggles to even hit triple digits. Even my 1978 LeSabre with the 350 got pretty darn slow above 90 MPH. A 307 even with posi-traction and 4.11 gears would be lucky to hit 60 MPH in under 9 seconds. Even the high-output 5.0 Liter V8 307 in the Olds 442 only made it to 185 HP. I used to have a friend that thought his 1977 Ford LTD could do 150 just because his long, ribbon speedometer needle bounced all over the place when he got above 80 MPH.
About the only GM cars that could hit 130 in 1983 were the Corvette, maybe the Impala/Caprice Police Interceptors and maybe the high output Camaros and Firebirds, and possibly the 1983 Turbo Buick Regal, but even that's a stretch.