Well, first of all, I think you are dismissing the surrender option somewhat lightly. The road junction at Spring Hill was seen by the Union commanders on the scene as absolutely vital, and if it had been seized by the Confederates, Schofield's army would have been essentially trapped with no place to go. They would have had few options, and none of them good ones.
The loss of Schofield's command..which numbered 20,000 men...would have changed the whole dynamics of the Tennessee Campaign.
--At Nashville in OTL...with Schofield safely in hand...the Union Army numbered less than 60,000. The Confederate Army numbered a little over 30,000 (they had detached a force under Forrest to operate near Murfreesboro, which meant the Confederates had a little less than 30,000 on the field at Nashville itself).
--A Confederate victory at Spring Hill means no Battle of Franklin. So they have over 6,000 more troops at Nashville, and the Union has 20,000 less. The numbers are very nearly even at that point.
--Pat Cleburne and five other experienced Confederate generals are still alive at Nashville, and another six are unwounded and in good health.
--The Army of Tennessee's morale, rather than being shattered by Hood's incompetence and disastrous defeat at Franklin, is running very high. The men have great confidence in their commander, and Hood himself has confidence in himself and his army.
So if the Battle of Nashville took place at the same time as in OTL, the result might have been very different.
However, I don't think Nashville does take place as per OTL. Thomas refused to attack the Confederates until he was absolutely certain of victory. He spent weeks marshaling his forces and building his strength up until he felt he was ready (indeed, General Grant was so impatient with Thomas about this that he actually was in the process of replacing him when the battle occurred). There is no way that Thomas is going to mount an attack on Hood's positions outside Nashville with nearly even numbers going into the battle. So...assuming Hood follows the same strategy as he did in OTL and puts Nashville under siege...one of two things happen.
1) Thomas continues building his forces and eventually attacks, perhaps in January 1865. Or...
2) Grant replaces Thomas with John A. Logan, who has orders to attack immediately, which Logan does. Given the relative evenness of the forces involved, and the much higher morale of the Confederate forces, the battle could go either way.
However, I would argue that a Hood who has been victorious at Spring Hill probably won't follow the same strategy he did in OTL. Hood's was extremely depressed after the twin debacles of Spring Hill and Franklin, and essentially became convinced that defeat was inevitable. It sapped his will to fight and made him indecisive. He put his army into entrenchments outside Nashville, retreated into this headquarters, and basically did nothing. That won't be the case here. He might well do as Grant feared he would do, slip around Nashville, and into Kentucky.
The Lincoln Administration will likely demand that Grant detach troops from around Richmond and send them west to deal with Hood. This might delay the conclusion of the war in the East, maybe even long enough for significant numbers of black troops to reach Lee's army, which would bolster the Confederate defenses there and delay the conclusion even more.
Of course, in the end, it won't mean much. Lincoln's re-election in November 1864 meant the Union would fight on, regardless. Even with a string of unbroken good fortune in 1865, I just don't think the Confederacy had four more years of fight left in it. So in the end, the war ends the same way...but a lot more people are dead.
