Since it goes away when you press the clutch, the TO bearing becomes even less likely. As does the input shaft and bearing.
If it was the input part of the trans, then it would do it in neutral too when the clutch was out, since it's spinning with the engine at that point.
So it could be an inner bearing on the idler or output shafts, or some gear-mesh issues between some of the gears. Seems like output bearings can take a beating.
Does it get worse in any particular gear?
When was the last time the lube was changed? What weight are you using in it currently? If it's been awhile, you should probably change the fluid and perhaps upgrade to a synthetic.
Heavier or lighter doesn't seem to be consistent in their benefits. Theoretically, a heavier grade would offer more cushion and fill larger gaps created by worn out parts. But I've actually had thinner grades of gear lube improve a transmission's noise characteristics before. It was not an NP435, but still, the thinner 75w/90 made it quieter (and it shifted better too!) than when I tried either the 85w/140 OR the straight 90.
On that note, all the NP435's that I've seen that ran ATF in them did make more noise than the ones running gear lube. Just a non-scientific observation on my part. Might have been the trucks were running less carpet and insulation in those cases.
You didn't by any chance remove any floor covering in your Bronco recently, did you?
Paul