Photoshop :: Changing Background On A Long Haired Cat

I have an image of a long-haired cat on a burgundy background.  My client (I kid you not) would like me to change the background to dark blue.
 
I fiddled with several methods but couldn't get the fine, long hairs that are in front of the background to look right. Eventually, I decided to try the selection/refine edge process...
 
I put a blue background under the layer with the cat on the burgundy background. I selected the cat, staying INSIDE the edge so none of the burgundy was selected. I went into Refine Edge and adjusted the radius until I had most of the edge fur selected.  This was about 75 pixels. I tried Smart Radius, but it didn't seem to make the fur selection any smarter...  So, I currently have it off . I then got the Refine Radius Tool and started doing a little selecting to get the fur right.  This is where I hit the problem.
 
As I select around an ear, for example, I can see the burgundy background show up.  When I release the selection, the burgundy disappears and is replaced by the blue.  GREAT.  BUT, instead of staying OUTSIDE the ear, the inner part of the ear ALSO gets turned blue.  The same thing happens all along the edge of the cat - sometimes I get a pretty good selection, other times the blue permeates the area I was selecting.  It's not 100%, but it's not ZERO percent either...  This MAY not be a huge problem in some spots, but it's a BIG problem, for example, in the ears.
 
So, I get done selecting, and I have blue around the cat. I click Decontaminate Colors to get rid of the blue and/or the burgundy from all around the cat.  It works in places - along sides and such where the fur is shorter.  But, the ears are still blue as are some of the longer tail fur. I ran the amount between 50% and 100%, and although the decontaminate gets better, it never gets really good.

Do and Output to a new layer with a mask, figuring I'll just clean up some of the problem areas on the mask.  Doesn't work.  I can open the mask. I can see that instead of having a white cat outline, I have a PARTIAL white cat outline but the face, ears, and some areas are shades of gray.
 
So, on the image layer, I take a white brush at 100% and try to clean up the mask, painting over the ears to have the fur and ear detail come back, but it just comes in as mush.  NO detail.
 
Am I using the wrong tool?  Magic wand is nowhere NEAR detailed enough to give me a really good selection.  Replace color leaves me with a blue background but burgundy edges.
 
If I'm using the right tool, am I just expecting too much from the tool?  'Cause whatever I'm getting, it's sort-of working, but not well enough for what I need.