I have had the same experience with the noise in/out of gear and it drove me crazy, near the bellhousing as you described.
My flexplate bolts came loose after a trans swap once and made a similar noise, so I checked there first. After not finding anything for weeks and hunting for it, I finally found it---- a stupid plate of metal that was tack welded to the passenger side of the exhaust y-pipe had broken off on one side and was ringing on the pipe.

Don't ask me how it makes a difference in/out of gear; something to do with the engine moving slightly?

Anyway it's hard to see but it's on the inside edge of the pipe facing the bellhousing. Maybe worth a reach up there to see if it's there at all.

Noise
 

My sound is more of a grinding sound. Like a few bolts on a blender.
On my flex plate. I have 3 bolts that are in right and tight. One that's at a slite angle. As the hole didn't line up right. No matter what I did. There was always one bolt that didn't line up right.
I was told that they changed the bolt pattern. By 1/16 of an inch.
So having a 93 motor in a 97 Dakota. With a 97 tranny. They don't line up. So I'm thinking I need to get a 97 flex plate. To solve my issue.

Same problem but it rattles in gear not park or neutral
 

I'm having the same problem except for a dose it in Is drive and reverse not parking neutral very annoying