Well, all in all, Grant did very well.
The reason why the south ran out of everything: Something to do with Grant's successful campaigns in the south and west.
The southern economy was regional. Most meats (cured for transport) came from Tennessee. Union victories in Shiloh, Ft. Donnelson, Ft. Henry, took the state from the rebellion. Anti-Confederate sentiment there was always high, as shown in part by refusal of one Tennessee Senator to resign, or to support the rebellion, and the raising of 56 Union regiments from Tennessee.
In response to those Union victories in Tennessee, the South began growing poultry on many small farms throughout the south, to replace the meat no longer available from Tennessee. This permitted Grant to travel without massive supply lines, feeding his soldiers on the poultry found on all small farms.
Grant placed his army south of Vicksburg, maneuver it between Pemberton and Johnston, and defeat them in detail. While Grand defeated Johnston, Pemberton counterattacked Grant's non-existant supply lines. I think of that as the most brilliant campaign of all time, certainly in North America.
Grant's initial assault on Vickburg did not take the fort. It did set up the city for assault, encouraged his men to work diligently during the siege. It also forced the south to stay ready for assault, slowing their ability to dig trenches.
A secondary source of meat was the states of Texas and Arkansas. Vicksburg completed the conquest of the Mississippi river valley, and blocked the shipment of meat from Texas, and Arkansas.
Cold Harbor. Surely, in hindsight the second assault was a mistake. But Lee had no reserves. If he thinned his lines, Grant would break them. If he shortened his lines, Grant would turn them. After Cold Harbor, Lee could not even offer a counter attack. Lee was limited to holding his trenches, accept the pounding, and direct the southern gentlemen to dig ever deeper. Cold Harbor had that effect, but I still morn the loss of brave men.
The south didn't "run out". They were beaten. I am sure this is a coincidence, but they just happened to be beaten, again, again, and again, every theatre where Grant was assigned. Grant beat his enemies in a campaign of maneuver that forced the southern generals to dance to his tune. And those southern generals, and their soldiers, could not keep up.
Lee was frequently the master of a battle, but never rose to the level of managing a campaign. His first assignment was unsuccessful, and he was known as "Evacuating Lee". Sharpburg, Gettysburg ended his only attempts at maneuver campaigns. If Lee could not manage a climactic battle, and win it, he was beaten. Lee was the last of the 18th century Generals, and in that light, he was certainly one of the best. Grant was the first of the 20th Century Generals, and his tactics, maneuvers, and strategems stand up well over time. Whether Grant's battles were win, lose,or draw, his campaign was successful.
And: Grant won. To the saving of the Union, the promotion of Liberty, and the great improvement of the world in general.
I wish to also address a frequent complaint of the Neo Confederates:
The great growth of the federal government came long after Lincoln. Though Lincoln put through an income tax, that was later found unconstitutional, and could not be used as a precedent. The amendment that legalized an income tax came long after Lincoln's death. The unconstitutional activities of the Roosevelt cousins, Wilson, and LB Johnson came long after Lincoln, and can't be blamed on Father Abraham.
Your theories aren't even worth debating. You give away your bias with the "neo-Confederate" remark. My theory is you are just another incarnation of Whiskey Papa.
Salt and Beef were from FLA, the "breadbasket" of the CSA.