Hi Involute, if you don't want to share the file publicly here you can e-mail it to me privately at moi@moi3d.com instead.
But yes as Brian says I'll need to take a look at the file to give you proper feedback on it.
Looking at a screenshot I can only make some general guesses - with a very sharp thin thing like that even a little tiny fillet can eat away a quite large area. You might try even smaller than 0.05 . Also if the filleter is having problems dealing with how to end the fillets you might extract those sharp pieces from the main object using Edit > Separate and then try the fillet on the separated part, that might give you something to work with since the filleter won't have to deal with how the fillet should interact with neighboring faces on the sides.
- Michael
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