The only problem with going backwards is that you are working from a drive-by spec at each step. You can tell students "this is the instruction set for the code you need to generate" and then "this is the intermediate language for the language you will parse."

None of the work is motivated concretely by the work of the prior step.

Fine if you are designing the representations for them, but I'm wondering how they would design an AST for a language they haven't seen or haven't thought about how to parse.

It would be an interesting experiment. If you were going to have them design the internal representations, you could have then move backward in a why that allows them to compile a family of languages. They could create something as general as the LLVM suite. :)