Some, or maybe all of the programs, if you’re rejected from Early Assurance you are considered for regular admittance. Some of the programs you then get a second chance at a combined degree, and all of them you can finish a B.A. and apply for the grad program alone.
So, I think that something like St. Joseph’s, that has a high acceptance rate for general admissions, can be both a likely and maybe a match for the combined degree program.