You don’ t have to be a non-degree seeking student. Many urban schools have a pretty open registration policy, and accept most applicants. My daughter just signed up for some classes at a 4 year university as a visiting student, but she could have transferred quite easily, and then transferred back to her regular school. You could attend for as long as you wanted (needed to) and then just transfer to one of the schools you prefer.
I don’t think you are going to have an easy time transferring to one of the schools on your list without building a solid record. If you think you can get into DePaul, why not apply there now?