Some nits to pick and things to add, because this is a cool topic.
(Thanks DakotaRanger

)
The biggest problem with the Trap door Springfield's was that the "brass", was copper which is why they had so much trouble with extraction, copper, being even softer than brass, could even be dented or bent just during loading.
While neither Reno, or Benteen were what would be considered "nice people", they were, as alcoholics, fairly representative of the Frontier Army of the day. Both , however, had outstanding records in the War, it is doubtful they would have intentionally left their Commander to his fate.
Ranks, during and after the Civil war could become confusing. Many lower ranking Officers were bumped up to fill holes left by resignations, until the 1900's Officers did not receive awards for bravery, they received a temporary promotion , called a "Brevet" rank, it was only valid for the duration of the war, then the officer reverted to his old rank, then other regular officers who served with Volunteer regiments would be granted higher "State" ranks.
If I recall correctly, Custer benefited from this system rising to the rank of General during the war, but on returning to an all regular Army and the canceling of all Brevets he reverted to his actual rank of Lt. Col.
What Custer planned was a standard cavalry operation . The Calvary were that era's "Rangers" or airborne, Lightly armed troops who could move rapidly using their speed as their armor and to enhance the shock effect of their attack.
Unfortunately he attempted it against men widely considered to be the finest mounted troops in the world.
When terrain and numbers prevented him from making a surprise charge through the village he lost all hope of victory, or even survival, when he was unable to scatter the Indians and break their organization. (the objective of the charge was not necessarily to "kill" their opponents, but to scatter them, creating disorder, Chaos, and break up their organization )
The reason for no sabers was that they were no longer considered an effective weapon of modern warfare by many Officers, including Custer.
As for the Gatlings, the decision was based on prejudice, Gatlings WERE NOT widely used during the Civil War, so Custer, not being familiar with them did not know that the battery was actually faster than his baggage train and would in fact, have had no problem at all keeping up.
As for Custers career situation, the 7th Cav. was the first posting he had received in sometime, because he was facing charges for his second (unauthorized) expedition to the Black Hills. He, like MacArthur later, had political ambitions, had he survived the Little Big horn he would have returned to Washington to either face a court martial, or to recieve the Republican nomination for President.