filing the nut is reversible.
You can fill up the groove with crazy glue, and let it dry up, or double/tripple/quad fold a piece of paper and get it under the string at the nut.
That way you could correct the string a bit.
Generally a string has a good height when it is between 0.4 and 2 mm from the fretboard.
The string should not cause extra buzz when filing off the nut, but does when lowering the bridge height.
*Edit: The E and A string are indeed at their lowest position. The D string could be lowered by 1mm, and the G string by 2mm. The only possible way is to file off the nut (of all strings). That would give you a lower action on the nut, and file off a bit on the bridge of the D and G string*
Lowering the string could result in the neck bowing backwards a bit, causing 'fret' or neck buzz; especially with the silicone strings setting the neck of the ashbory might take weeks before it takes on it's final shape.
Even with a regular bass, adjusting string and string tension could lead to the neck bending over time, as much as a week before the neck has fully adjusted itself.
I'd say to be very careful with filing the nut, don't overdo it, and give the bass a week to adjust.
This for future readers,as I see that the original topic is nearly a year old..
