Also, the Railroad Station Historical Society, (which on occasion even errs in a listing), shows this building as M&St.L Ry.
Hmm. It appears some mis-described information was passed my way. After trading several emails, we discovered the pair of us were talking about two different things. The M&St.L engine house is indeed there, but in a different spot. He misunderstood what I was describing. So, yes. It is apparently RI, built after the roundhouse was demolished in 1953. Thus RI=> C&NW=> UPRR. (At least I had the last two correctly noted above.) The M&St.L engine house still stands, but a couple of blocks east of there. Thus I did correctly name the active RR company there, as requested. Do I get partial credit?
Partial credit granted I did a closer look to the place, and there is a building that could have been that engine house you are refering to. It's next to S 12th st where 7th Ave S runs into it. It's without railaccess.