I haven't heard anyone say "escape goat" but to be a"scape goat" is to have things blamed on you or laid to your charge and that's Biblical but if you think about it, the original scape goats had the people's sin's laid on them, then were set free in the wilderness and the other goat, chosen by lot to be the "sacrificial goat" was slaughtered.
I had a business partner whose wife used “escape goat” frequently, and it was hard not to show amusement. She mangled a lot of figures of speech above and beyond those sourced to the KJV Bible. “Taken back” instead of “taken aback” was another favorite of hers. She was not Christian and was first generation American, with parents from eastern Europe. Very smart and savvy in many ways, but she mangled the language.