Agree, the kickdown is purely there to downshift during hard acceleration. On mine the adjuster goes loose by itself no matter how hard I tighten the lock nut (too lazy to get thread lock free from work!). But every now and again I just readjust it. After adjusting I can take on the Japanese imports with their turbo lag and beat them across the traffic lights.

I am always careful when it comes to free checks, they will only do it if they can make money out of further work.

I've had my 144 for 6 years, my father bought it new in 1971. Can't speak for my father, but for the past 6 years the transmission had always shifted hard when accelerating hard, shifted soft when driving gentle. Modern transmissions have slip built in during gear changes, smoothing out the change. The BW35 does not have this slip. Actually, slip is listed as a fault condition!

The BW35 has 2 brake bands that are adjustable. Easy to do according to my manual, but I have never done it. This may or may not fix your problem, too tired/lazy to think now. Others might comment with experience.

I would suspect a broken transmission (or engine) mount. Or worn spider coupling (center bearing, whatever you want to call it) in the drive shaft. My '71 144 had the spiders replaced about 2 or 3 years ago, the guy told me they fell apart in his hands! My car was clunking like metal on metal at the time, that went away with new spiders.