727 one bad clutch plate. Input to output washer half gone

OK/wait!....
was the broken thrust washer still captive on the pin of the output shaft? and
Did you check the end-play of the input shaft before tear-down?
Cuz I'm getting an idea.
If the washer was out of place,
this would allow the input to move backwards,
which could have allowed the first clutch in, to drop off the splines, (thus no longer indexed). And so then going into Third gear, the clutches would no longer be flat, but with the dropped clutch forcing a twisted engagement, the discs would be now driving on the outer edges. In that state, it wouldn't take much power to make them slip, and burn up/cast off the friction material or just run out of clamping..
With most of the fiber clutch material now gone, the piston would go out as far as it could, but the out of place disc would stop it from clamping
Meanwhile, with the washer out of place, the input moved to the back and the planetary was cut.
I think we got it!
My TFs have all had a tinned-copper over metal Thrust-washer; now I know why. I highly recommend, lol, to not put a fiber washer back in there.
Did you see the picture of the Not Flat steel plate?
I'm thinking you were right that it dropped the first clutch off .
But I would expect the splines on the inside edge of the friction to show damage.