Using the peak thrust of the motor you are treating the case of the rocket being driven into a perfectly rigid barrier. If the rocket accelerates, that is to say if there are unbalanced forces, then the compressive force on the airframe will be less than the thrust delivered by the motor.
And the other side of the stress-strain relation is the strain, which is the fractional change in length of the body under stress. Moving the cross-section aft, means a shorter section of tube and a proportionally smaller deflection under the compression.
If you look at the Euler formula to which nytrunner directed us,
https://www.continuummechanics.org/columnbuckling.html
the critical load -- the stress under which the column fails -- goes as the reciprocal of the square of the length. The mass of the rocket above (and the force needed to accelerate it) would increase as the length of the forward segment. Which means, as you take cross-sections further down the rocket, the buckling strength of the aft section increases faster than does the load it must support.
A couple of months ago (or maybe longer) a related top came up on the mailing list of the club with which I fly. Somebody in that discussion posted this reference
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690013955.pdf
I tried to read it, without much success..
As nytrunner pointed out, its a deep dive to deal with this stuff.
Yeah, there is certainly way to make this into a differential equations problem. I think, though, that since the body tube is going to be homogenous and of uniform cross-section (piece-wise, anyway) that you could figure the compressive stress and buckling strength at each transition or discontinuity. It wouldn't be much fun, and I don't think it would be necessary. My guess -- based on the fact that rockets built with LOC paper tubes do fly successfully on J motors -- is that the tube will not buckle under stress. Some other part of the rocket is more likely to fail.
Thanks. It does sound like fatigue, but I really don't know enough about this. The OP will have to comment on whether longevity is a concern.