My (limited) experience is that if the Army stays together, it will coordinate through each zone they move through together. This makes for one hell of a threat.
In Shiloh, Take Grant's Arnmy of the Tennessee and put the reserve artillery in it.
Create a Corps using Lewis S. Wallace and another using E. McClennand.
(There is a trick and maybe a bug to breaking McClennand out. You can't just divide him in place - you have to double divide. Divide once, then pull the McLennand divisional unit out of the McLennand Command you just created and then divide again to free him up for Corps duty.)
Evenly distribute the Divisions, calvary, and supply between them. Be sure to give each of those Corps one each of the divisions with leaders in them. I have found Sherman with Wallace to be a rock solid combo.
You've got yourself a meat grinder with a lot of tenacity and talent.
The goal is not to focus on the territory to take (or even to protect, let the CSA divert itself in your rear; it won't matter), but to destroy the enemy's forces. You destroy his capacity to fight, and the territory will follow.
Go down towards Corinth one zone at a time, together, using co-ordinated move order. Use the VP sites to focus the battle; to draw the enemy to battle.
Meanwhile;
Deploy all the naval units into Clarksville.
Move the Army of Ohio and Crittenden towards Humboldt, through Forts Henry/Donnelson on turn 1.
Take G. Thomas' Corps from the Army of the Ohio onboard the fleet on Turn 2, and sail to Memphis. Assault Memphis on Turn 3. Bring the fleet to offer bombardment support to the Army of the Tennessee by moving it on Turn 3 to wherever Grant and Company happen to be, and move with them.
By Turn 5 or 6 you should have Corinth under siege, and of had some close but successful battles north of Corinth in turns 3, 4 and maybe 5.
On or about Turn 6, take your 3 Corps (you did move G.Thomas towards Corinth on turn 4, didn't you? Leave the sharpshooter behind to garrison Memphis) and the Army of Tennessee with all its reserve artillery and assault Memphis. You should have 3-5 battles that first give you more losses than the CSA gets, but becomes a route for the CSA by the last round.
Bask in Glory when this turn ends.
Using this method against the AI, I can get a victory by shattering the National Morale most of the time.
Oh, why your are at it in turn 1, for what its worth, buy some replacement Line Infantry and Cavalry; 12 Line Infantry and 10 Calvary is what I buy - that gets me to near 0 conscripts.