I had the exact same symptoms, and my problem turned out to be the o-ring that went between the engine block and water pump. You do have to pull the pump to get to the O-ring, so the pump may as well be replaced.

It's a DIY job (albeit lengthy), and can be done from on top of the engine, but the four hex-head bolts holding the pump to the block are tricky to get to. There's little clearance for the ones on top, and the ones on the bottom aren't easy to see from above the engine, and you may end up unfastening the wrong ones.

Be sure to order the correct pump, the Laso one I received (from this site) is missing holes for two sensors on top, I'm going to have to order another one with the additional holes.

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Steven Harrison

1993 300E2.8 - 196K
2001 E320 4MATIC - 86K