1. Check the wheels and tires (there is a difference as the wheels are the metal doughnuts in the middle of the rubber): it’s possible that one of the tires could be smaller than the others and it could be setting up a resonant condition with the driveshaft. Also, make sure the wheels are all the same size.
2. Check the wheels: it is possible that one of the wheels could be slightly out of round and, again, this could be setting up a resonant condition (they both vibrate together), causing the feeling you describe.
3. Check the half-shafts on the front end: if the half-shafts are out of true (they are not perfectly circular as they turn), then it is quite possible that the resonance is being set up there and being transmitted through the body structure.
4. Check the driveshaft: it is possible that it could be slightly out of round as a magnet or weight could have shifted, setting up a slight vibration that is resonant with the body structure and causes the low rumble you are feeling.
Of course, there are many other places to look, however, when this condition sets up it is more than likely the driveshaft causing the problem as it interacts with other parts, such as the half-shafts, bearings (if they are out of round, then a resonance and rumbling will set up as you describe).
The good thing is that I honestly doubt there’s much wrong with the transmission. It’s a mechanical issue from what you have told me.