I still think you should invest in a pressure washer, even to clean the star emblem.
Since you're only taking your car to a car wash about 1/2 dozen times a year, you will bring out the rust bug in your W124 rather quickly especially in the 4 season climate where you live.
I live here:
Johnstown Building
There is no water supply for us to use. I have a garage, with HOT water at the overhead heater(10 ft), but it's a 3 car garage with the drain under the vehicle next to mine, and the other owners might complain. The car wash is really my only option.
What makes you think washing the vehicle at a car wash(at least once a week!) will make it rust? I don't think they recycle the dirty water. If they did it would be filtered. We have 2 season climate here, Cold, and COLDER. We actually get less snowfall than the panhandle of Texas, surprisingly, but they do use a lot of salt type products on the hilly parts.
The biggest concern I have is stone chips on the front end, since they throw tons of cinder on the roads for traction. Windshields are big business around here.
I'm considering some undercoating of the vehicle in the spring, maybe some Bedliner material sprayed on all the critical points, wheel wells, welds, joints, seams.
My previous experience with German cars is plenty of rust to be expected, especially when they did that factory undercoating of 1/4 inch thickness, and water/dirt gets under that rubberized product. I haven't really been under this unit yet, so I can't tell you what is there. I'm hoping it's bare metal, or a thin coating of an oil based product. The Monroni Sticker doesn't show any undercoating, and I don't see any evidence of undercoating in the engine compartment. I presume they put wax in the doors/trunk lid, or tar, I just don't know.