



Hi Edwin,
i can´t claim to be familiar with the inner workings, but the symptoms described may be caused by a relatively small problem. In the "keyless works" of a movement, there´s a lever accounting for "switching" between winding and timesetting functionality.
Here´s a picture of the keyless works found in a AP 3090 caliber:
As one may see, the stem drives a small wheel with a recess; the lever touching this will "recognize" the crown/stem position (winding/setting) and in years of use, sometimes it can "slip" out of the recess.
Such will keep the keyless works in the last position, which means it is "blocked" and thus only setting or winding can be done.
It´s probably recommendable to ensure a fine watch as a Lange timepiece only those sufficiently trained and experienced on these; inappropiate service can cause more problems than cure and it really deserves the attention it got during initial production.
Assuming it is out of warranty, there may be a choice of sending it in to Lange or to have it repaired locally.
Adjusting the keyless works (if such caused the phenomenon) is something many watchmakers are familiar with. So if there´s not more, turnaround time from your local Lange AD will be much faster.
On case refinish, the outcome often is a visually new watch afterwards.
If you don´t mind those signs of wear to vanish, then why not!
Just that it needs to be send in and probably will taker longer to get it back.
On the differences, the decoration seems to be different?
The circular graining ("perlage") on the base plate, but the engravings on the balance cock as well?
Cheers,
Peter