I'm wondering if there might be any weaknesses in the Confederacy that could play to the Union's favor, ones that never had time to arise IOTL. The most obvious would be some kind of major slave revolt. I doubt Lincoln would be willing to actually start one himself (although he probably could if he gave Harriet Tubman enough guns), but if one arose on its own with reasonable leadership...
There are certain weaknesses in the Confederate position that could be taken advantage of, not that inciting a slave revolt is one of them. One of the reasons British observers entertained ideas of an intervention in 1863 was precisely because of that reason. Besides, as someone said, inciting a slave revolt would probably turn 50,000 bayonets against the Union overnight and torpedo a lot of support for the war. If one arose on its own... well let's just say Lincoln would not exactly be in a hurry to extinguish it...
Could the Union try nibbling off the outlying regions? Hold the line in the East and take the Mississippi Valley? Link up with the pro-union sections of Tennessee and North Carolina?
As the situation currently stands, the outlying regions like the Indian Territory and Arizona are currently in Confederate hands because of 1) better luck in 1862 and 2) the paucity of resources the Union can devote to those territories. The line in the East is currently the Potomac immediately south of Washington and so Lee's army has to be driven back to at least where it was at the start of 1862 for the capital to be safe from potential embarrassment, so expect a Union offensive in May 1864. If they can drive them back, it may buy time.
In the West, there's room, but the Union suffered a terrible reverse on the Mississippi the previous year and - well, you'll see in the catch up chapters from the Western theater coming up - they have to go farther than they did historically. If they can bottle up the Confederate fleet, they could certainly attempt some amphibious operations to disperse Confederate forces and discomfort Richmond, but that will take time to organize. There's options, but none so good as they existed in OTL 1864.