I wouldn't waste my time or money on a starter. If the engine is cranking over and it isn't slow or bogged down, the starter is fine.

This sounds like a fuel delivery issue. Does this car still use the CIS injection system? If it does, you may have an issue with the cold start valve, or you could have a problem with the fuel accumulator under the car.

If you have the latter, the fuel system will tend to vapor lock, especially if it's worst after it's sat 30-45 mins after you shut the engine off from hot and try to restart. The fuel pump doesn't "prime" like newer cars do when you turn the key, so you will have to crank the engine until the pump builds pressure and allows the engine to start. Went through this with the SL a few years ago and when I finally replaced the accumulator, the difference was night and day.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]