-->As always<-- , mileage numbers are a general target number , mileage numbers are a marketing tool.
The signal strength at you location of KCWX is strong enough to be received by the long metal reception elements of the CS600.
However I can not say for 100% certain that reliable reception will happen.
There are reception situations where the only way to find out for sure is , Try It.
If you buy from places like ,
http://www.solidsignal.com ,
http://www.amazon.com.
The price is low for the CS600. And ask if will take the antenna back if it does not do the job.
In part , I am responding with antenna recommendations based on what will work , sometimes I give the reasons why , And I am responding to what you say is happening with reception.
When I give some reasons why , Many people Panic , It does not mean , throw on the brakes and stop and not go forward. (So mostly I do not go into the in's and out's of reception)
Reasons why are not a world stoping event , the reasons of the reception situation are like a balancing act of the situation , and is the Green Light to forward.
If I did not think the CS600 would work , I would not recommend it.