Sorry for not posting sooner but this has been a bit of a challenge for me. As I've said before I'm a people person not a unit person. As best as I can tell from cross referencing work the soldiers listed in the NPS system as 3rd Battalion, Missouri Infantry are listed in the Missouri SOS system as having served in the 6th Missouri Infantry Regiment. Names and ranks match but company designators are all over the place. They all seem to also have served in the Missouri State Guard 3rd Division or 8th Division which may be where the confusion starts. "B", "3", "8" all look alike in bad handwriting, poor typewriters, and marginal microfilm.
I may be all wet here but with that leap of faith observation made, the Thomas Proctor you refer to is listed as having enlisted in the MSG at age 16. He fell ill after the Battle of Lexington and was left behind in a house near Greenfield, Dade County. He eventually joined the 6th MO Inf Reg. and was killed at Kenesaw Mountain Georgia June 27th 1864.
Therefore to answer your question directly I don't think the Thomas Proctor of the NPS 3rd Batt'n MO Inf. is the same Thomas Frazier Proctor of your inquiry. I'll keep hunting.
John Russell MD