If only the tip is missing then, as soon as you start doing anything to it, you're down into the triangular section where there's lotsa meat.
I would thing you're right: centre it up, drill into the triangular section, set in a new pin, silver-solder it in place, contour to fit and then cut it off and round the tip, right at 5.6". Should work.
Working from mine, precise diameter of the actual firing-pin tip, the part that whacks the primer, is .0774", but I really don't think they were all THAT critical. (If they had been, nobody could have made them!) But that's what mine measures, according to Mister Moore & Wright. Likely there is wear to take into consideration.... mine was REALLY through the Pacific campaign: nowhere nearly good-enough looking to go on television!
Keep us posted, kindly. This is interesting!
Hope this helps.