I know one thing for sure Red.  If you put a shadow on the outside of a tag you plan on making transparent, it'll all turn to black or it'll look downright horrible, lol.  So if you did put a shadow on the tag, try it without a shadow.

 

Animation Shop changes all pixels that are less than 100% transparent.  It can diffuse them and/or change them all to white for instance, depending on your Optimization Wizard settings.

 

The only other suggestion I can make is to give you my Optimization Wizard settings.  You can try making it with these settings and then change them back if it doesn't help, but these settings won't help anyone much if you still  have a shadow on the outside of the tag.  You can have a shadow on the inside of your tag, just not on the outside edges.

 

Here are my Optimization Wizard settings.  I see that Yvonne has supplied hers too, LOL.  So, I'll say, try them both and see what you get.

 

Also....click on "Optimization Wizard" and run it in AS, first, then check the animation again and if it looks ok, save it.

 

 

These are my Optimization Wizard settings:

Page 1.  Optimized Output
.  put a dot in the circle for "Animated GIF File" (obviously), lol
.  put a dot in the circle for "Create a new animation from the optimized animation

Page 2.  Animation Quality Versus Output Size
.  click on "Customize"
    -  "Number of Colors" set at 255 colors
    -  make sure "Optimized Median Cut" is selected.
    -  Reduce colors by - make sure "Nearest Color" is selected.
. click on "Partial Transparency" tab and make sure it says
    - Convert pixels less than 1
    -  Would you like to blend the partially transparent pixels?
        .  make sure "Yes, blend with this color" is selected and select the color White.
 . click on "Optimizations" tab
    - And make sure that only these two boxes are checked off:
        .  Write Minimal Frames
        .  Collapse Identical Frames

. Click "OK"
. Click "next"
. Click "next" again
. Click "next" again

and view the new animation

If it doesn't look good you can always make a change here or there and try it again.
If it does look good then you can save it.