School me on trans basics

When the oil comes back from the cooler, it think it does not just "dump into the pan". It first goes thru the lube circuit, which is regulated to peak at about 30 psi, but it is a function of the convertor pressure, which is factory regulated to about 75 psi.
The cooler line and fittings are easily able to handle the flow in the lube circuit.
If your TC is ballooning at cruise rpm, imagine what it might do at Full-load WOT!
Perhaps tour TC regulator valve is not working right.
Perhaps your thrust bearing is going.
Perhaps the inspection cover is not staying where you expect it to.

A small vibration that you can control with throttle, I imagine is more likely to be in the U-joints, the pinion angle, or the mounts, or perhaps the tail-bushing.

You say the TC is a 3500. But. Have you verified this?