I have a ’53 Pontiac and am replacing the gas tank. The old tank had cloth straps that fit under the metal straps and between the tank and body. Your video for the 57 Desoto gas tank replacement showed no such cloth straps. What purpose did they serve and are they necessary?
Many cars used a cushion between the straps and the tank also between the tank and the frame/body. Their purpose primarily is to prevent squeaking. Whenever two pieces of metal are in contact with each other there is the potential of them rubbing and squeaking.
I have seen some cars over the years that were designed in such a manner as when the cushion is removed the tank fits loosely in the straps, however this is uncommon. The ’57 DeSoto you mentioned used no cushions originally and the tank fits tightly in the straps.
If you are absolutely committed to a accurate restoration, I would encourage you to replace them with similar material. If not, your car should be fine without them as long as the tank fits tightly when installed. If you do decide to reinstall the cushion material, I would consider replacing it with rubber, as the old canvas type hold moisture and in time look shabby as the material gets exposed to dirt and water.
Here you’ll find a link to a source for rubber tank strap material.