We have discussed these consolidated units on several occasions, and I'm still confused about the date of organization.

Various dates of organization have been mentioned as:

-The 1st, 2nd and 3rd Arkansas Consolidated Regiments were organized ... about May 17, 1864
In October 1864, applications for staff officers state there has been none since the "Brigade" was organized on May 17. This inidates the date the brigade was organized, but not necessarily the "consolidated regiments

-July 22, 1864 HQs 1st Consol regt W W Reynolds LtCol cdg-Dockery’s bgde near Monticello-Lt Scott 14th Ark [Powers] now part of 1st Ark consolidated- to be dropped-absent without leave since 2/1/64-appd Dockery & Fagan

-In September 1864 the consolidated regiments were formed

-Several units were consolidated and ended up designated the 3rd Inf. Regt. Consolidated, Trans Mississippi Dept. on Nov. 29, 1864.

However, the September 1864 return appears to be the first "official" documentation that we have found thus far.
Gen McNair
1st Ark consol-Lt Col W. W. Reynolds
2nd Ark consol-Col T.J. Reid
3rd Ark consol-Col H. G. P. Williams

This would seem to eliminate Nov 29, 1864 as date of organization for these regiments.

What do you think is the most likely date of organization for the consolidated regiments?

Of course, I agree with you that topics such as this one are as you say: "one of those huge black holes that plague Arkansas researchers."