But the only time we had a problem with a pressed penny was using an older (70's) penny. It definitely was harder and resisted being pressed so it was hard to see what we were trying to have imprinted -- you could still see a lot of the original face and back. The new pennies press much more distinctly (unless you are wanting it to still look like a penny?)
We just culled them to use the newer-looking ones. They are still going to "turn" somewhat so the cleaning, etc. is not going to make a big difference in the long run, and depending on what you use may actually make the pennies more susceptible to tarnishing.