Thanks for the thoughts.
I'm hoping that it's possible to let Muay Thai corrupt my karate, rather than the other way around. We have a lot of leeway in sparring (yes, most people are all bouncy-bouncy like in that video of RurikGreenwulf's cousin, but some people revert to boxing style movements, and get away with it). Kata has to be done "right", but it's trained more like dancing.
Our body shots are decently powerful, which is where my bad habit of dropping my hands comes from. Most people either don't punch to the face, or punch just "towards the face" because they're worried about the "touch contact" rule. So I respect the power of body blows and have no incentive right now to protect my head. I was hoping Muay Thai would put that right, plus teach me how to punch in a less telegraphed fashion.