The cap is supposed to be dry. It sounds to me like it is leaking and needs to be replaced.
No, you are not crazy trying to adjust the shift quality by backing out the modulator. I just did this on the 91 300E (211k miles) AND adjusted the bowden cable to where it shifts very nicely. Actually I am amazed I have driven it almost 100k miles with a too firm shift.
The only thing you want to watch out for is the flaring (slipping). As long as it works properly enjoy.
I would replace the vacuum modulator.
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)