Your car would have a 904, end of story. If your car is original, it would have a push button, cable operated shifter, and no modern slip yoke INTO the transmission. Instead it would have what is called a "ball and trunnion" front U joint.
You could put a more modern 904 or 727 either one behind the 340 but the trans MUST be made for a small block V8, and MUST be a "long shaft" version.
Mopar bells in the years we normally find here come in three series............... only for slant six, ........... only for the small block v8 series (273-318-340-360, and can be adapted to operate with 5.2/5.9 Magnums) ................ and the larger B/ RB "big block" transmission
Early ball and trunnion:
http://www.earlycuda.org/images/Tech/Ujoint/trunion1.jpg
You can easily ID a 904 from a 727 by looking at the pan. A 904 is rectangular with one corner nipped off. A 727 has an additional bulge on the passenger side pan rail. There is more to it than that. Lots of details over the years. EG the 65 transmissions (rare) were cable shift but used a slip yoke. 66 and later were mechanical shift linkage and all slip yoke. Up through 68 or 69 or so, only the neutral safety switch (single contact) was on the transmission. Later models used a 3 terminal NSS, with the backup lamp switch in the switch as well
some transmissions were so called "lockup" You can ID them if you look at the input shaft. The "regular" trans has splines all the way to the end of the shaft. The "lockup" has a smooth nose on the shaft, like a stick shift pilot shaft
There is long and short tailshafts, the short being used in some motorhome trucks, and the special adapter housing used in married 4x4 transfer cases
And some later ones if you have (like mine originally) a console floor shift, need the mounting on the bottom of the tail housing for the shifter linkage bracket
