I have a 1999 C280 that did exactly the same thing like yours. I don't know if the solution will be the same, but I had my mechanic lube the starter drive gear and the flywheel about a month ago, so far (knock on wood) the problem hasn't come back.

There is a TSB on this:
DDAF15_30-U-640 Starter Occasionally Does not operate.
The starter stops running before the engine is running due to lack of grease on the starter drive gear.

I had that done with 2 hours labor. $120. Cheaper than changing the starter.

I hope this will work for you.