The simple answer is in your allowance for one side to not matter. As said, a rolling mill will make short work of this, but you can do the same on the anvil with simple tools.
Take a silver 1$ coin and anneal it by heating to dull red, air cooling to black, and quenching. Next, mark a line on the back side with a marker on the axis you want to stretch. Now, set the coin with the face you want to keep down on the anvil. Place a 1" to 1.5" piece of smooth round stock on the center of the coin, and strike with a 3# hammer. Move the round stock a bit and repeat, going from one side of center to the other, repeating till you get to the end. Use the line drawn to keep the stretch going the direction desired. Repeat as needed. Anneal again each full pass, and when done, anneal one last time. The face side will be nearly unchanged beyond the stretching of details. The back can be left as is, or filed smooth.
Note, if your anvil is chewed up, put a smooth plate of steel on it to be the face against the coin.