Thanks for the additional suggestions. I will try that next time because I already advanced further. Where do I get brass wool?
In the meantime I made some progress. I disassembled the movement and cleaned the parts. The first picture shows them before cleaning. The next after cleaning in Zep fast 505 in the ultrasonic cleaner. After 10 minutes at 50C the parts showed just some signs of cleaning, i.e. visible brass in spots. I had to add two more 10 minute cycles until the parts appeared to be clean. I turned out that the rust was more superficial than it seemed, so I skipped the Evaporust step and went to remove surface rust and did some polishing on the lathe. For parts that couldn't be de-rusted or polished on the lathe I used a stainless steel brush wheel on a Dremel. I didn't remove the strike levers from the wood frame because I was concerned that the steel "hook nails", that hold them in place, might brake when I try to remove them, with parts of them left in the wood.
For the wooden parts I tried my intended rug and acetone approach, but it turned out that the layer of grime was just too much. So I switched to a stiff brush and denatured alcohol (methylated spirits) and washed down the wood parts, wiping with paper towels until they remained clean. The wood appeared rather dry after that, so I rubbed it with some mineral spirits and followed up with a soft brass brush. That gave the wood a nice matte shine.
There were two repairs that I noted were necessary after cleaning. The click and click wheel of the strike side were very worn and not reliably functioning. I disassembled the wheel, re-shaped the click and cleaned up the click wheel with a file. It should be good for the next 100 years now. The other repair was for the escape wheel. One pivot was only about 1.5 mm long. To make up for the missing length the brass bushing was somewhat pushed out of the wood panel . So I re-pivoted that wheel and pushed the bushing back. Everything else looks quite ok now.
I will report back when I have the clock back together and working.
Uhralt