I'm not a Haskell expert, but I am a sat expert, and worked with good Haskell programmers. We managed to get decent performance, but what we ended up with looked a lot like a C program translated into Haskell, so it wasn't clear we had really gained anything. Memory safety I suppose.
"Like C, but with memory safety and QuickCheck" sounds like a pretty good language for a SAT solver... "Idiomatic Haskell won't produce a very fast SAT solver" is something that doesn't surprise me.