I wouldn't go any further than 1 inch from the header flange (I think 3/4 is usually recommended) This gives you the closest read of combustion event. I use an open element thermocouple (exposed tip), and I have also noticed that what seems like even one single miss-fire or dead compression stroke will throw raw cool fuel out on to the sensor showing a low blip on the recording.
I have had my EGT probes in this location for about 13 years now and have only needed to replace one. And that's because it seized in the header and I couldn't get it out. Otherwise they are pretty tough and hold up well to the environment they are subjected to.
When placing the bungs, don't drill the hole first! Use a nut, feral and piece of tubing to extend out a "handle" to hold the position and angle you desire while spot welding them for placement. Then get them all where you like them, then complete the welds.
And then finally twist in the fitting and drill through the center of both the fitting and bung to put the hole in the primary. Drill the hole slightly oversize. don't worry about this oversizing much. The seal happens at the nut and ferrule. If the fit is too tight, you will never be able to get the damned things out when you need too. Carbon deposits or just plain bad luck will seize the thing into the header. Trust me on this.
Also, it is good practice to face the 90 degree turn on all the probes perpendicular to air flow. Try to set the probe tip depth as close to center of the pipe as possible before tightening the nut.
Something like shown in attached.