I don't think smallblock 727s are the same but my Chassis book is buried so someone else will have to reply.
The 904 transmissions were different for different engines.The one I'd pick for your car was behind the high perf 360s, the A999, IIRC. It had the most clutches and would definitely hold up to the 340 you have outlined. In case you don't know, the 727 eats more power than the 904 variants. Plus you can get the 998 or 999 with a 2.74 First gear which I'd pick because it'd allow use of one step lower (numerically) gear in the rear and leave the line the same.

For bigblocks I'd pick whatever Transman told me to do.
R.