Lass doch die beiden Sätze dann so, auch wenn sie beide etwas abrupt und unelegant dastehen.
Yes, or make them into one sentence with a colon:
... draws its appeal from the variety of new approaches (used): quantitative, statistical, comparative, economic, and frame analysis.
If these are only some of the approaches, then
... approaches used, including ...
I think that "analysis" (singular) may be OK, meaning that the authors use these various types of analysis.
A different point:
The book edited by Miller and Rhodes draws ... -- without commas --
may possibly be correct, if the phrase "edited by M and R" is defining/restrictive, i.e. if it serves to distinguish this book from some other book/s.