Perryville: only troops engaged?

[Stryker65]

Hello all,
In honor of the Perryville anniversary, I'm thinking about making a small order of battle for the engagement, but it seems that not all the Union troops were engaged. Here is what I've found from Battles and Leaders:
1st Army Corps:
- 3rd Division (all troops)
- 10th Division (all troops)
2nd Army Corps:
- 6th Division (21st Brigade only)
3rd Army Corps:
- 1st Division (2nd and 3rd Brigades, and Artillery)
- 9th Division (1st and 2nd Brigades)
- 11th Division (all troops)
Cavalry:
- 3rd Brigade
Are these correct? Have I missed any? I know all the Confederate troops were engaged; at least, all the brigades were.

 

[mobile_96]

Used Hafendorfer, noting casualty lists to indicate units involved, if not fully, then at least nominally.
Buell's escort
4th U. S. Cv
first Army Corps
3rd division
9th Brigade
17th Brigade
28th Brigade
Unattached
2nd Ky Cav.
1st Michigan Engineers and Mechanics
10th Division
33rd Brigade
34th Brigade
2nd ArmyCorps
6th Division
Edward McCook Cav Brigade
7th Penn (4 companie)
3rd Army Corps
2nd Brigade
10th Indiana
3rd Brigade
9th Division
30th Brigade
31st Brigade
11th Divison
35th Brigade
36th Brigade
37th Brigade

Captain Ebenezer Gay's Cavalry Brigade
2nd Michigan

 

[Stryker65]

Now, I have a question about the command structure of the Tenth Division. As many know, the division commander (BG Jackson) and both brigade commanders (BG Terrill and COL Webster) were killed or mortally wounded that day; Jackson first, then Webster, and then finally Terrill.
I have found that Terrill was killed before he was able to formally assume command of the division, and thus was not Jackson's successor. However, Webster was not made commander of the division either, and thus the divisional adjutant did not communicate the chain of command clearly.
The brigade chain of command is stranger. After Terrill's death, Colonel Hall took command, but after the battle, Hall became temporary division commander, and did not leave any evidence on who his brigade successor was. Colonel Theophilus Garrard would be the next ranking officer, but his detachment was only in the brigade temporarily, as remnants from the Army of Kentucky. Colonel Thomas G. Allen would then be the highest ranking brigade colonel left, but he was wounded at Perryville as well.
On the other hand, Webster's brigade command fell to Lieutenant Colonel Silas A. Strickland, which is itself strange since Colonel William P. Reid was the next ranking officer in the brigade.
My idea is:
10th Division: Brig. Gen. James Jackson (killed) ... Col. Albert Hall (after battle)
33rd Brigade: Brig. Gen. William Terrill (killed), Col. Albert Hall, Col. Theophilus Garrard?
34th Brigade: Col. George Webster (killed), Lt. Col. Silas Strickland (did something happen to Reid?)

 

[mobile_96]

(did something happen to Reid?)

According to Noe, Reid and his 121st Ohio were left behind to help bury the dead. They were there about 2 months. Neither Noe or Hafendorfer explain why Strickland got the position. In the ORs Reid is only mentioned as Col of the 121st. There are also no orders or reports from Perryville giving Strickland the position.