Simple solution
The USA should drag itself into the 21st century and use chip and pin. It's not clear to me why retailers, visa or customers tolerate a situation which allows cards to be cloned so easily or the virtually non existent security checks that happen at point of sale in the US.
Chip and pin isn't foolproof but it would stop card skimming / cloning which must surely be the most common cause of credit card fraud by a long stretch.