EIN and SS# regarding Chex

I got put into Chex thanks to check reordering by BOA when I was not working. I could not catch up in time and they closed my account. They have since lost a class action lawsuit because of that but that is another story. I posted this question last year but never received a definitive answer. I want to open up a business account with an Employer ID Number (EIN). My question is: Will the bank accept the EIN only to open my account or will they deny the account because of my SS number and Chex?. If I was the President of the company and opened a separate account and sent a VP to do it they would not want his SS number or mine. Just the EIN. Why would it be different for an individual? I asked a couple clerks and they said I can't open an account with an EIN if I am in Chex with my SS number. The problem is that when I asked the question they knew because I was asking. If I simply went in there with the EIN and filled out the papers I do not think they would run my personal info.
I am hoping someone has a definitive answer because clients have been insisting on paying by check and it is a pain in the a-- having to either cash them or deposit them in my wife's account. The bank won't allow me to deposit them if her name is not on the check. There are no non Chex banks in NJ. Or any second chance banks either. Thanks for your answers.