I don't know what type of transmission you have in your 300E, but I had a similar problem with my 1991 420SEL (W126), which uses a 722.3 version tranny. Over a period of about a year, reverse engagement time got longer, until it was multiple seconds. Finally, reverse engagement degraded to the point where it was not engaging at all if the tranny was hot (but still engaging if it was cold, after 4 or more second). Engagement of Drive remained fine, as was shifting in forward gears.

On this transmission, this symptom is usually related to worn out B3 reverse clutch plates. Since repair of the B3 clutch requires removal of the tranny, and opening it up, you might want to do a full rebuild while you are at it, especially if you have a lot of miles on the car, AND intend to keep it for a while.

But, it is possible to just repair/replace the B3 clutch plates, and save some non-trivial money. In my case, the transmission shop said that the rest of my transmission looked good. He advised to do a rebuild if I intended to keep the car a while, but that just repairing the B3 clutch was also a viable option, and that it was not leaving any "ticking time bombs" inside. Here in the SF bay area (land of high prices), cost was $1300 for just the B3 clutch repair, versus $2600 for a full rebuild. Most other parts of the country would be cheaper for both alternatives.

Good luck,

Bob Schleicher