Simpson's Six-Month Militia makes sense--that service would have been sandwiched between the dismantling of the earliest home guard-type units in the summer and fall of 1861, and the founding of the Missouri State Militia in December 1861 (few of the Six Month Militia regiments lasted six months).

I've had my research in storage for several years, and recently pulled it out. As I go through it all, I'll keep an eye out for the Murdoch documents.