Before you buy any parts for this one make sure it will physically fit in that 66 Barracuda. Maybe do a test install. I do not know that answer, but maybe somebody tell us if they used one of these in an early A body.
Notice in your first picture there is a steel strap (snap ring cover) with two phillips head screws holding it to the tail housing, and it is running vertical. At the top screw there are extra raised strengthening ribs. Those are not on passenger car or early truck and van transmission tail housings and it is very close to rubbing or making contact on a later 67-76 A body. I have one of those in a 75 Dart Sport and it does fit in mine but is very close.
That style of 727 is a good one to use if it fits your application. The 904 you have is plenty strong enough for an early A body. Do you need an upgrade to a 727?