My compliments to your use of OR series IV as a source. It contains great information not included among records of battles and campaigns in series I.
To summarize, General Twiggs had intended to use at least one company of the LNG to escort Federal prisoners from the New Orelans rail depot to prison. Evidently this was public knowledge and accounts for news reports you listed that the LNG (at least one company) would be present for the event. Twiggs later decided against their use and sent General Lewis official notice to that effect on Sept 29, 1861. An account in the New Orleans Bee mentioned in a previous post does not list the LNG among state militia escorts.
Of course the LNG company initially tapped to be on hand could have appeared in an unofficial capacity, but at this point we have no evidence of that.