Welcome to the forum Walther.
If it backfires, i would spend some more time checking the ignition system.
You said you have checked the ignition distributor and rotor.
From what i have read on this forum, these parts are responsible for a lot of problems if they're not working perfectly.
I know how expensive they are, so the best thing would of course be if you could borrow the parts from a fellow 300E owner or from an extremely kind shop, just to make sure they're not the culprits.
Have you got the correct spark plugs? (ie. NOT the Platinum plugs) And are they in good condition?
Bad/corroded electrical connections?
You can spend a LOT of money tracking down defective parts on a 300E. -Take my word for it! So try the cheap stuff first.