I believe rust's safety guarantees are enough to ensure the soundness of passing data to/from interrupt contexts and interrupt handler re-entrancy. See rtfm[0] for an example and a good explanation. I think DMA handling can be made safe by using the right abstractions, and then you'd just need to trust that any piece of code that accesses the memory uses the abstraction instead of accessing it directly.
Checking interrupt priorities sounds like an interesting problem. What is the state of the art in deadlock prevention? It would also be cool if you could tell the compiler "I need this interrupt handler to return in less than n clock cycles." I wonder if someone could write a rust compiler plugin to check that.