I had the same phenom. on my '90 300E...the oil consumption, or loss, suddenly became a concern when the oil light came on one day. In between the next 2 or 3 oil changes (every 5000km), the car started to need 2 full liters. I also would see a puff of white smoke if I 'gunned' the engine.
At about that time, the car needed a periodic emissions test (provincial law), which it passed, but the hydrocarbons emissions were now up near the high end of acceptable (150ppm, max. allowed 200ppm).
I saw a post here about valve stem seals needing attention and decided to look into any product that could help, before looking at any more large scale engine work, worth a 10$ try, I figured.
I found an oil additive that promised to address this exact problem at the nearby automotive supply place. It is called "CD something-something", in a not-easy-to-miss package with neon all over it...sorry for the lack of precision.
I'm now over halfway to the next change of oil, and I have had no noticeable loss of oil.
Maybe it, or something like it found in your parts, could help you.