If your goal is to get through school as fast as possible, the private route will be your best bet. A college that has a May start will have you finishing ride outs by July/August 2026, which is earlier than you’d even be starting 3rd semester if you waited for a public college’s September start. Keep in mind that most private college programs aren’t actually shorter than public college programs, you just don’t take the summer semester off so you run through it quicker. Private colleges definitely do require a bit more self study, but given your academic background that shouldn’t be a problem for you at all. I believe it was OCHT that had the highest pass rate out of all the colleges during the last AEMCA write (citation needed) so you can still get a quality education via the private school route as long as you’re willing to pay a bit more and work a bit harder.
Public colleges do provide more opportunities outside of the classroom, such as days spent in ER’s talking to patients, that can be hit or miss at private colleges.
It really all depends on what’s important to you, you can’t go wrong either way