For what's worth, I'm running 37" MTRs. Was running 35" Duratracs. The vibration didn't change. It also didn't start until long after the Duratracs went on. Sounds like it is not the transmission since you have an auto...

 

I lowered tire pressure from 37 to 32 and my cyclical hum gets better. 65-75mph my wife says it sounds like a base drum. At 26psi I cant feel it. 26psi is what I crawl at. Factory 13 rubi wheels and tires.

 

I did the chalk test on the new tires and found that at about 35 psi I had the best contact. So my cold pressure is actually closer to 33 psi so once the tires warm up a bit they're right in that 35 psi range.

 

Not trying to be a turd or a master of the obvious, but... FWIW

In addition to the removal of retaining clips and cleaning the mounting surface, there may be one more thing so simple it might have been overlooked: When installing lug-centric wheels without hub rings, it is very important to tighten lugs progressively in a star pattern before final torquing. If one lug is torqued down tight by an installer before the others are seated, then it just may be that the lugs (and hub) are not all centered correctly in the wheel bores. You will get vibration from this, and eventually the lugs will loosen and the problem will get progressively worse; I have seen it happen when an installer is inexperienced or just plain in a hurry... it's worth a look.

Best of luck.