HUMMING NOISE

It very well could be as poster #2 says

But I'm gonna tell you a story of what happened to me.
I'm going with a bad pattern on the coast side of the R&P. Sometimes that's just the way it is. My 3.55s have been doing it for all of 25 years.
It's not really a bad pattern; I've adjusted it twice; and I think I can read a pattern pretty good having worked on an assembly line for a few years. In my case, it's the way the gears were cut, there's nothing I can do about it.
Now I gotta say, Poly Bushings seem to make it louder.
Here's the story;
A friend of mine was looking for a used 3.55 chunk, and learned that I had one in my car. I was willing to sell him those gears ; but I knew they were like this, so I took the friend for a ride, to showcase the noise. I mean in my car it was hardly noticeable. and so, he was satisfied and we made the deal. IIRC, the deal was that if he didn't like the 3.55s, I would pull them out and swap him for 3.23s, but he would pay for the work. IIRC he had 3.91s that I took in trade.
And so, I transferred the chunk out of my car (68 Barracuda) and into his (71 Challenger), and sent him on his way.
Some short period of time later, he shows up at my door complaining of this noise, so we went for a roadtest, and holy cow! those gears were way louder in his car.
So, I had to swap them back out, for a set of 3.23s I had. Which made him very happy.
Meanwhile, after the summer of his gears in my car, (big fun) I swapped that 3.55 chunk back into my car, the very same chunk, with no changes; where it's been most of the time since.
Anyway, in the end, my friend liked the dead-quiet 3.23s better anyway.
As it turned out,
My car had and still has, the big HD rubber front eye- bushings, whereas his had Polys from a well-known company.
In my car, what little noise there is, comes up the driveshaft into the trans. Whereas
In his car, the noise came thru the bushings and into the body. There was no way anybody could sit back there; it rang like a bell on deceleration.
I cannot say with authority that this is your problem, cuz there are still a few more possibilities.

Like:
1) Ima thinking the front input bearing, maybe.
but it should not be sensitive to which direction the power is travelling thru it, and so, in my experience, when it gets noisy, it does so in both directions.
2) pinion angle could be the cause of it depending on how far nose down it goes, which is controlled mostly by the flexibility of the springs, and the cylinder pressure of the engine and amplified by the rearend ratio.
3) ATF will let every imaginable noise out of the box, whereas 140EP is a pretty good noise damper.
But ATF will shift way quicker.
I use a 50/50 mix to help the clusterpin live.
4) If Oldmanmopar is right, and he very well could be;
In the past, I have milked some extra mileage out of a worn but not pitted cluster pin, by flipping it upside down and end for end; then reslotting for the woodruff key.
So if you can't get a new pin in a reasonable period of time, consider that an option.
BTW, swapping out that pin is a full teardown.

5) Or I suppose, like I do, just drive it.