The bonded washers will probably work fine but bonding to metal can be a little tricky. My advice would be to put a lot of effort into surface preparations before you glue them in. Alternatively, there are some proven bonded fasteners on the market (Click Bond CG596, etc.) but they tend to be expensive.
I forgot where the carbon fiber is located on the door. In general, you want to make sure that you keep the carbon and metal apart to avoid corrosion. I'm not sure if this is a factor for the door handles.
Since your washers have a large flange, it might be possible to bond them in place, then put an additional ply of glass over them. You can fill them with clay, layup the glass, then knife trim the opening before it's fully cured.
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David Shelton, Aerospace Engineer and Soaring Nut.
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