You have plenty of spare rep, you should be using it on guns, IMO. However, you could probably still win the battle because the Union only starts with a small portion of their strength. And positioning matters more than numbers. Its easy to outflank the Union on this map.
As far as army composition goes, you really spent a lot of money on support units. Expensive LeMats and Spencers don't do a lot of good if you don't have enough infantry to hold the enemy in place. I find that for melee cav, you might as well just stick with Palmetto/Sabre all the way because it has a higher melee value than anything other than LeMats, for a fraction of the price. There are unconventional strategies with lots of cav, but generally speaking the vast majority of your force should be infantry.