I'll explain the method to my madness so someone else can try since I have a killer headache and have run out of ideas.
I'll be using Mercury as the example:
Step one - take Mercury's piece (the one with the symbol for Mercury)
Step two - Go to the first letter, aka M, and line up the symbol with the letter. That will give you CO and RV on the outer and S on the inner.
Go through and find the letter that corresponds with the last hole. In this case, it's the letter C. Again, line up with symbol with the letter. This will give you U.
Now you have CO, RV, S, U. Start in the top right of the most outer ring, going clockwise. You will get: CORVUS - as the U comes before the S. Make sense?
This method falls apart with the other ones that I have answer for - Neptune and Earth. But I get the letters the same way, and then anagram them out to get Vulpecula and Lepus respectively.
My other letters for reference are:
Saturn: ANX IF L A G
Venus: A L IC I A (this is a genus of a seasponge so I thought maybe it was possible as an answer)
Jupiter: M I R G A (kind of means mouse??)
Have at it.