Denied for Non-Accredited School—Need Advice from Fellow RNs!

I'm applying for a lot of nursing positions, but unfortunately, my ASN school isn't accredited, so many hospitals are denying my application. I'm currently enrolled in an accredited BSN program that I'll complete in August. My question is, do hospitals typically ask for transcripts to verify where you went to school?

Would it be a problem if I just listed a different school for my ASN? I know it’s technically lying, but it’s frustrating that hospitals focus so much on accreditation. At the end of the day, we all take the same NCLEX, and I passed it, so I’m just as qualified and safe as anyone else!