The connie is a difficult one as it not a standard brush finish, I don't quite know how do describe it, it is very delicate, almost like a japanese rice paper finish.
I have cape cod but think that would be far to strong for this finish.
Personally I have found sunshine polishing cloths to be the most gentle and yet at the same time able to take out minor scratches without ruining the finish.
http://www.sunshinepolishingcloth.com/
When you say quartz do you have the normal 15 second a month one or the double eagle perpetual which I have. Comparing the two is the equivelent to comparing an ETA movement with a Patek movement IMHO!
I am so happy with mine, it is performing much better than quoted specs, looks like I am on for +3.5 seconds a year accuracy
Here are a couple of pictures of mine, we don't have enough Connie pictures!
And an idea of the brushed finish on this watch
