I don't think the filled slot would have any effect on tuning, but if the slot is too shallow the string could slip out with a hard strum.
Each of the items listed in your final paragraph could contribute to tuning instability. Taken together they're a recipe for disaster. You can get adapter bushings from Stewmac to make your Klusons fit in the 10mm holes.
"Chisels are calling. Time to make sawdust."