Trench warfare
did occur late in the Civil war. The Siege of Petersburg is one of the most famous examples. Both armies had fairly static trench lines that reached for miles around Petersburg and toward Richmond. Although both Armies lacked anything resembling machine guns, or at least one fielded in large numbers, field pieces armed with canister shot and trenches filled with rifleman shredded the opposing army. The Union army did attempt to penetrate the enemy lines using both sapping,
and massive human wave type attacks.
Many of these images are very reminiscent of the First World war.
In the end both sides made a "race for Richmond" but the Confederacy lacked the manpower to do this and the city fell. The trench warfare around Petersburg lasted 10 months.
A timeline that has the South and North facing off across no mans land isn't that far fetched. As you can see above, a barbed wire analogue did exist and was widely used. Early land mines were used, mostly just impact shells that were buried. Many hand grenades types were used widely in sieges,
and even early attempts to use chlorine gas as weapon Many different types of "machine guns" were used or invented during the Civil war even if they were not widely used.
So as you can see, there are large amounts of possibilities. With only a little tweaking, I'm sure you can make very depressing timeline.