I suggest removing the manifold and adding water to prove conclusively where the water is getting into the inlet port. It can't be the centre stud as that is between Nos 2 & 3 exhaust ports.
The implication is that the threaded bar you removed went through into the water jacket (As it should) but then further on and through the wall of the inlet port. If that is the case you should be able to feel the hole with a finger in the port.
It seems to me that the problem comes from removing the threaded bar which has opened the hole in the port. In all probability your repair to the manifold stud is done correctly but it doesn't seal the hole left in the port.
Manifold studs only have sufficient thread to do the job and so couldn't reach into the port.
If you take out the new stud you'll be able to tell if the old threaded bar went in a great deal further than the new stud. Also you'll be able to tell if it protrudes into the port as it should be possible to feel it in the port.
If this is the case then you might well be able to use a short length of the threaded bar you took out to screw into the hole in the port. As it apparently sealed before it might well do so again.