I have been working with the various militia units in my work in Missouri's guerrilla war, since the militia units were often the first line of defense against the guerrillas, and your question about "why so many Mo. militias in the latter half of 1864" falls directly into my area of study. I should preface my remarks by stating up front that I am no expert on Cochran's 6-month militia. I am trying to make input into your question about "why so many Mo. militias in the latter half of 1864."
I found something more compelling that the draft, more compelling that the Union command's wish to slowly restore civil law in Missouri in order to stop the guerrilla war, and more compelling than other reasons I have been toying with. The answer I have developed is simple fear.
Let me explain. During the spring of 1864 Banks' Red River Expedition in Louisiana failed and Banks had to withdraw. Also, Steele's Camden Expedition in Arkansas failed and Steele had to pull back his forces into central and north Arkansas. Further, the Union military was stretched thin in its campaigns in the East, in Georgia, in Mississippi, in Tennessee, etc. and pulled some troops from all over the Western Theater to answer the need other places in the Western Theater. This was an economy of forces move. This forced the Union military to draw in its forces in Arkansas that spring to concentrate them where they could better deal with the remaining Confederate forces in that state. Therefore, the Union military in Arkansas abandoned some of its bases in northeast Arkansas, such as Batesville. This, in effect opened the back door into southeast Missouri should a Confederate force so decide to go there.
Of course, with Missouri's General Sterling Price as of March 1864 in charge of many of the Arkansas Confederate troops, someone eventually with about 12,000 troops DID decide to take that back door into Missouri in a bid to end the Union occupation of the "Show Me State." Part of the plan was also to make the northern voters weary with the endless war frustrated with an unexpected southern victory in Missouri and vote for the Democrat peace candidate, George McClellan, in the coming November 1864 national election.
All of the above was not lost on the population, especially the southern part, and the Union leaders in Missouri. Very large number of guerrillas and Confederate recruiters infiltrated into Missouri starting in the spring of 1864 until by July Union forces in Missouri were under great pressure, especially in northeast Missouri, and desperately needed more troops to keep all these southern irregulars at bay.
Unfortunately, in early 1864 the Missouri General Assembly's investigation into the conduct of the Enrolled Missouri Militia and it's offshoots like 1863's Provisional EMM, revealed that these militia forces were poorly trained, poorly led, and their local depredations were antagonizing much of the rural population and making enemies out of former friends. Worse, some of the EMM, such as the "Paw Paw Militia" or two regiments of the EMM (81st and 82nd EMM) just north of Kansas City as well as many other portions of the EMM in northeast Missouri and other places were infiltrated by southerners and were no longer reliable as Union forces. Some of these were willing to protect their own communities against bushwhackers but would not resist regular Confederate troops if they were to come into their geographic areas.
The Dept of the MO commander, MG Rosecrans, therefore sought to re-invent military service in Missouri by creating whole new types of units such as the Citizen Guards of his General Orders Number 107, I think in June 1864, with the simple strategy that they would only protect their communities and not conduct offensive combat. To make new troops Rosecrans in August created several new regiments of Missouri cavalry (39th through 51st regiments), some with one-year enlistments to which northern sympathizers in the EMM and other remnants of other militia units flocked to in order to serve more effectively--that is, to kill Rebels--and to keep local guerrillas from killing themselves if they remained at home waiting for the guerrillas and whoever else to come for them. As you suggested, having these eleven new full-service, full-time cavalry regiments also nicely took care of the draft question. Several of those regiments eventually left Missouri and did good service on other battlefields. Further, some of the more reliable old EMM units from the program started in summer of 1862 continued to soldier on in some parts of the state, often with good effect. Granted, many of the old EMM and PEMM militiamen joined these new cavalry regiments, leaving some of the older militia units much smaller than earlier. There was little loyalty problem with the men who committed to these new units such as had been the case with the former militia units that allowed their members to remain at home on their jobs and respond only to crises in their home area. In other words, General Rosecrans was desperate for troops and invented new ways of getting them. He also begged for Kansas militia to come to MO and help (which Kansas pointblank refused to do until Price's army approached and threatened invasion of Kansas). Rosecrans also begged Illinois to come to Missouri's rescue which they did with 100-days cavalry regiments which were good for some things but not for others. In essence, the northern cause in Missouri had its back to the wall, and came close to losing the state by late September 1864 when Price's army of about 12,000 came calling. Now you see what I mean by "fear."
At least, that is my cornball theory about why all the different Missouri militias and other troop units in 1864.