It was good to distinguish between force and pressure.
I’m not sure if the “pounds per square inch” thing is just hype confusion, or if there really is something meaningful to measure there (like using knuckles or hand positions to reduce impact area and thus increase pressure, which might be significant if some effect of receiving punches depends more on pressure than force, eg: breaking strength). I suspect that this might be important for something like “why do people use brass knuckles?” - as they would reduce the receiving area and thus increase the pressure (and might reduce the deceleration distance as well, see below).
(Four square inches seems kinds of small for the impact area of a boxing glove, tho)
But let’s get back to your first pass at decoding all this - comparing force. Force in this case doesn’t seem very meaningful as a primary measure either. What you have is a given mass (hand and possibly some of the arm) moving at some velocity, which is going to be decellerated in some distance - which will yield some particular force. The faster the same punch decelerates, the higher the force. That is, the same punch landing on a soft bag will have low force, and on a hard bag, more force. Or - the same punch will have more force against a shoulder than a gut, or a hard skull than a yielding jaw, even if perhaps less damage.
The primary measurements of a punch strength would be momentum (speed times mass) or possibly kinetic energy (proportional to speed squared times mass). Given the former PLUS the firmness of the impact, one can derive the force as a distinctly secondary factor. Force is also time varying - a pulse from 0 to some peak and back to zero, with a varying curve and duration = hard to compare - while momentum or energy at start of impact are relatively simple and comparable between punches.
The only way to make force meaningful would be to have a standard for the combined resiliance of the gloves (and/or fist itself) plus the receiving surface. Absent that, the peak or average deceleration “force” is meaningless to compare.
So - it seems that your answer only partly sorts out some sense from the publicist’s pseudo-scientific hype about various fighters.