Actually I'm having some thought about emphasizing the readiness status as less "combat fatigue" and more "mental damage from contact with the supernatural". You know, Cthulhu style.
What I'm thinking of is leaving everything as is, except on missions with no "supernatural" enemies (aliens etc.) you don't lose Readiness. This can be done by applying an effect every turn which adds +1 Readiness, thus cancelling out the loss.
Bear in mind it's a just loose idea for now.
Maybe rename readiness to something like "stress", "paranoia", "calmness" or "uneasiness" so that it makes more sense, since readiness doesn't really seem to explain that well what the mechanic does and fits more with what you want to do. Do note that "stress", "paranoia" and "uneasiness" should use an inverted logic from the current one because the more of those you are, the more likely you are to react unexpectedly to stimuli.
I don't think the analogy to Cthulu does make sense, though, as non paranormal events could cause such reactions from soldiers too, that's just my opinion, though.