Don't forget that if you push the same amount of shot to the same velocity, the one with "Lowest max chamber pressure" is likely going to have a bit higher pressure down the bore where that thin spot is than one with a bit higher chamber pressure.
Once you get beyond round 4" to 6" from the breech actual bore pressures do not vary my much, regardless of the load.
To get the absolute lowest pressure down where that thin spot is use a light shot charge, lower velocity or both. Then use a load which gives the "Highest Chamber Pressure" compatible with the gun's proof.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra