I doubt it's an issue with the box. But on that subject it might be worth getting yours sevices btw.
But tbh, the only rumble like you describe that I've encountered was on Entwood the king pikeys car. Eventually cured when the dif was replaced. Iirc.
Mine was far more severe than described ... it didn't stop at 50 mph, it just got louder !!
It also got worse very quickly over a fairly short time/distance
There was never any vibration felt through the steering either.
It "might" be worth you trying what I did to eventually trace mine after a rear wheel bearing change made no difference....
Jack car up both sides as high as you can get it SAFELY on to good axle stands, then using bottle jacks or similar jack the wheels up (I used the bottom shock mount) until they are sitting in the "right" place relative to the wheel arches - you could always measure this before and after - I just guessed). This gets the drive shafts etc into their "natural" position
Now, hand brake off, run the car and drop it into gear .. on mine it very quickly settled down at just under 40mph without me touching the throttle !!
I could then crawl under the car and listen for the 'orrible noise ... quickly apparent it was the diff .. and pulling on the handbrake cable each side to stop each wheel in turn was pretty conclusive as well...

Diff changed and all went quiet !!
Now, this might NOT solve your problem .. but it might eliminate the "back end" as the source and just leave the front as suspect
