727 TF Big Block Push button Transmission plus other parts!

I agree with krazykuda. As far as I know, all push-button transmissions used a cable-shift, which yours doesn't have.

My 65 Newport 383 has the 1-year only cable-shift BB 727 with sliding yoke output. It also has a column shift, which was unique as well.
My 65 Dart has a cable-shift SB 904 and the flange output for a Detroit ball & trunnion U-joint.