Engine vibration

I'll guess bad convertor or misalignment.
In Neutral or Park, with the car stopped ; The entire Geartrain in the trans, and in the GVod are stopped and not turning. The only things in there that are spinning are the front pump, the forward drum, the hi-drum, and the sunshell. You didn't mention the vibration quitting in Second gear, which anchors the hi-drum and thus the sunshell also,so that just leaves the forward drum, which is the smallest diameter.
In reverse the hi-drum and L/R band is applied, and the forward clutch is disengaged, so now only the outer case of the forward clutch is spinning at or near engine rpm, plus the planetaries. You did not mention vibration in reverse, so I'll go out on a limb and say the trans is fine.
That only leaves the TC.
And I'm sure you thought about that when you installed it, so it is either neutral balanced and the flexplate was balanced to the engine or vice versa, right?
Well in my thinking, that only leaves two things;
1) the guts of the TC or it's bearing. or
2) a misalignment of the crank centerline to the transmission centerline.
I have never had to check this
but I think the only way that this can be checked is by complete teardown of your transmission, the installation of a flatplate on the crank (like a flywheel) and then bolting the empty case back on. Now it's set up for the dial indicator.
Next remove the sparkplugs, and slowly by hand, turn the engine over watching the dial needle. You are looking for a readout in the pump-register of .007 or less. To change it, you remove the factory dowels , and install offset dowels in their place.
If you find yours is in spec, that, IMO only leaves the convertor. Sorry it couldn't be easier, but you already did all the "easy" stuff.
Happy HotRodding

Let this simmer for a while; there are smarter guys than me here that might think of something else.

OOps treed already,lol