Hmmm Kreg 1 router 0
I don't use screws anywhere near I think I will be routing. Since you glued it you could have removed the screws before routing although this would have left a hole to patch.
Bottom line - bummer
For edge trimming/banding, that would get rounded, or the like, I'd go with biscuit joints or a splined joinery and glued---
without any screws, brads or nails.
In edge banding, there are times, when one cannot get a ''closed'' tight fitting joint, so as to get an almost seamless appearance. To accomplish the feature, the surfaces would need to be super-straight and smooth, otherwise there'll be slight gaps, or hair-line cracks, which will need to be filled and finished---
tough task for many to accomplish.
Screws may not draw the joints tight enough, to achieve a closed/tight fitted seam.