I would loupe /eyeball each drill, which would only take a few seconds each and might turn up some bad grinds.
Look for clearance up to the cutting edge...and ballpark clearance..point looks on center, and the chisel angle is correct.
There is a good chance the points are circle-ground or just pressed that way to the angle, and then the clearance or heal is brought up to the edge to sharp..if the back-off does not come fully to the edge they are likely to break.
One experiment you could try is to "break in" the drills in a VMC by turning a piece of scrap material into swiss cheese.
A VMC will generally provide more controlled conditions than a live tooled lathe. Drill 1000 holes to slightly dull the edges and stress-test the tool before moving it to the lathe and see if that gets rid of the anomalies. Sure beats running a lathe unattended overnight, only to scrap the entire lot because a drill broke at 7pm.