If permanently attaching the strands to the LED is ok; you can drill holes in the LED face. CA them in place, and you've got great light transmission. It's a big help to have flat top LEDs, but possible with standard cases.
I drill about .010" to 0.020" deep in the face, dip the strand in CA, insert, and wait for it to cure.
Black everything out, and install.
I don't have pictures of the process, but here is one of a proof-of-concept model using the method. (didn't care about this one, so it isn't blacked out.)
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