Has anyone ever heard of/been able to have their application for an independent study course/placement considered and accepted after the deadline has passed? If the details for a independent project/placement is fully thought out, how likely do you think admin will accept applications past the deadline?

Just try and see - you don't really have anything to lose.

I did that this year for independent study. The coordinator didn't like it but it got approved in the end. I think I was about a month late and I had to give a good reason as to why it was late.