The problem is not the "base" engine torque. The problem is torsionals. The actual engine torque is not constant; it fluctuates as the individual cylinders fire. So if the nominal engine torque is (for example) 500 ft-lbs, it may actually be varying (rapidly) between maybe 470 - 530 ft-lbs. That variation is called torsional vibrations (or simply, torsionals).
The level of torsionals changes with load and engine speed. Torsionals are highest at low engine speed, and maximum torque. So the worst case is heavy throttle (high torque) at low engine speed. Let's say the TCC capacity is 1000 ft-lbs (I'm just pulling numbers out of the air for this example). If the max nominal engine torque is 850 ft-lbs, then maybe with torsionals the actual peak is 950 ft-lbs (still OK for the TCC).
I'm thinking perhaps there is a problem with his TCC. For example, if his TCC capacity were only 930 ft-lbs, it would slip (shudder) if the torsionals pushed the peak torque to 950. Apparently 3rd gear is the worst case because engine speed is lower than in 4th or 5th. That means torsionals will be higher. Using our example, suppose the peak torsionals were +100 ft-lbs at 1365 RPM, but only +70 ft-lbs at 1500 RPM. Then his TCC would shudder in 3rd (at 1365 RPM) but not in other gears (at 1500 RPM).
Now admittedly this is all conjecture on my part. But my point is: Yes, the TCC capacity is the same in all gears. But the level of torsionals (and therefore, the actual engine torque spike peaks) will vary with engine speed, so if engine speed is lower in 3rd, torsionals will be higher, and therefore TCC shudder may exist in 3rd but not in other gears. If he's getting TCC shudder, then either his engine torque spikes are higher than normal, or his TCC capacity is lower than normal. Not low enough to cause problems in most driving, but low enough to give shudder at the point of peak torsionals.
If he holds it in 2nd gear longer, then his engine speed in 3rd will be higher, therefore torsionals will be lower (hopefully low enough to avoid the shudder). So delaying the 2-3 upshift doesn't "fix" the converter, it just reduces the peak torque spikes. Hope that makes sense!