Allen, several Texas cavalry units were reorganize into dismounted cavalry in the late summer of 62. I'm not sure when the 16th Texas was dismounted, but it may have happened in August of 62 at Camp Crystal Hill about 5 miles upstream from Little Rock on the Arkansas River. The Texas Cavalry units that were dismounted there, had men assigned to take some of their horses back to Texas while the rest of the horses were used in other capacities in Arkansas. Their saddles and other equipment was stored in a warehouse in Little Rock. A lot of these Texas cavalrymen did not take lightly to being dismounted so a number of them tranferred to new or other mounted units. Here is one possible guess and I say guess, that John was assigned to or volunteered to wrangle the horses back to McKinney, Texas in August. He then ask for a transfer and got one, then joined the 5th Regt Texas Partisian Rangers in Sept of 62 back at McKinney, Texas where he had joined the 16th Texas Cavalry about seven months earlier.
Here's a question to ask, if he still held the rank of Captain in the 16th why would he go back to a Private in the 5th Texas Partisian Rangers, unless he had lost his rank when the 16th was dismounted. This is what happened to a number of Arkansas soldiers after Shiloh, the confederate army was reorganized in May of 1862 at Cornith, Ms and some Arkansas officers lost their rank (voted out) and came back to Arkansas and joined or formed new units in Arkansas.
I've placed a lot of speculation in the above, but it gives an avenue to take a look down. Is John M. McKinney the same 30 year old soldier in both units, we need to find out. At one time he or they were Lieutenant's in both units. The same name and the same small town, joining a confederate cavalry unit a few months apart looks like the same man, but may not be. You said you looked at several cenus, what about a pension or a widow's pension from Texas. A close look needs to made into the history of the 16th Texas Cavalry. I've not seen much on Martin's Regt Cavalry (5th Regt Texas Partisian Rangers) but it needs to be looked at also. Somewhere there's a record out there to fill the gaps.