I'm still not completely certain MLIR addresses the difficulties I face, which is exactly to design the specific IR that can express the passes I need. Having outside constraints seems like it would just make this work harder, and I'm not sold that the reusable components offered by MLIR offset this. At some point I probably will try generating MLIR from the compiler midend, though, just to see whether it might be a good idea.
The thing that concerns me the most might be that using MLIR seems to require writing your compiler in C++. LLVM can be accessed by non-C++ languages just fine, because it's just a consumer of bytecode, but the whole point of MLIR is for the IR to be extensible, and that will presumably require custom C++ to introduce the desired bespoke structures. In comparison, it's rare that a compiler needs custom LLVM passes.