In '97, the 5.9 Magnum used a weighted flex plate. As stated, the '97 torque convertor will not work with a '72 727. What you need is a 727 neutral balance (not from an LA 360, as they had weights welded to the convertor for balance- which, btw, is completely different from the balance for a 5.9 Magnum- more on this later) torque convertor, which you will bolt to your 5.9 flex plate. One hole in the flex plate will need to be oblonged (5 minute job with a rat-tail file) for the convertor to bolt up.
Now, about that LA 360 torque convertor. As mentioned, 360s had the balance weights welded to the convertor, 5.9s were balanced via the flexplate (from the factory), and so used a neutral balanced torque convertor. You can use an LA 360 TC if you remove the balance weights, located on the face (engine side) of the torque converrtor between the nounting lugs. Depending on year, there will either be 1 large or 2 smaller balance weights- remove them. That will make the TC "neutral balance".
If the TC comes from a late '72 or '73 340, you will encounter similar balance weight issues; address them the same as a 360.
Any 318 or '68- early '72 340 will be a neutral balance TC, and ready to use as-is.
Be wary of using a big block 727 convertor, as some of these used an 11" convertor which will NOT fit your Magnum flex plate.
