Last month, I submitted a paper to the American Review of Math and Statistics (ARMS); however, recently, I learned that its parent company, American Research Institute of Policy Development, is a predatory journal that accepted my paper last week. They requested that I submit a publication fee of $200 to a (very likely) sketchy bank overseas and that they will publish it at the end of this month. I have emailed them three times asking them to withdraw it (though the first two times they did not reply at all; the first time I asked them to withdraw it while they were still reviewing the paper, but they basically responded with them accepting my paper a week later with no edits to be made and a completely anonymous peer review). My third response today was the following:
"Good morning. I am sending you this email reminding you that I am withdrawing my paper from your journal. I will not pay you the $200 publishing fee (or any publishing fee for that matter), and I do not give you permission to publish the paper as I still hold the copyright. I hereby am once again withdrawing my paper from your journal, and if I do not receive a response from you by June 20th, I will consider the paper withdrawn from your journal."
I have also not signed any copyright agreement with them (though as per Q18 in ARIPD's FAQ here, it looks like I retain copyright no matter what). If they don't publish the paper by the end of the month, then I might be okay, but what happens if they end up publishing my paper regardless of me not paying fees/signing any copyright agreements? Am I basically "locked out" of submitting to other more legitimate journals? Thanks!
EDIT: The acceptance letter also includes the following information regarding payment:
The last date of payment for the scheduled publication is June 20, 2023. However, you may make the payment later for publication in future issue. Contact with the executive editor in that case.