I would mix up some thickened epoxy with some fine saw dust.

I've tried that - using saw dust (from the table saw). I found saw dust was too coarse to use as an epoxy thickener- I couldn't get it to fill small spaces and it was surprisingly 'stringy'. It may depend on the saw blade used, but I think any good sharp blade will produce shavings, not dust. Sanding dust (from the sander bag) might be a better choice, though i usually find the dust includes bits of abrasive grit.
Even better would be 'wood flour' additive sold by some epoxy suppliers.
WEST filleting mix is a brown color; it's another possibility.
I think some folks have used flours from the grocery store like whole wheat and rye flours. As long as it mixes well with epoxy, it will work. Do a few experiments and you'll find something you like.

You'll probably have to re-sand after filling, but it shouldn't be a long job with a ROS or soft disk sander.

Turn any clear-finished kayak upside down on a sunny day and stick your head into a hatch. It won't be unusual to see a few rays of sunlight shining through- it wasn't unusual in my boats, anyway!