I bought the wrong transmission for my 66.

Seems like you trans is out of an F body or pickup.
A short tail shaft A833 is correct for the Dart. Yep like you know, shorter than that OD trans, thus tail shaft issue.
Question? Is the bolt pattern on the OD bell the same as needed for the A833 trans? Check!!
Also check the input shaft cover in the A833, it should be smaller than the OD unit. Issue again.

B & T suck. You ain't gonna hurt any trans with a slant.
I was under the impression that a833 bolt patterns were the same at the bell. What is the input shaft cover?