BST = Base Stat Total. It is the sum of all a unit’s stats if they are an unmerged, Level 40 5 Star unit, not counting their weapon or any equipped skills. The amount varies depending on if the character is melee or ranged as well as their movement type. Melee armored units generally have the highest BST, while ranged cavalry and ranged refreshers have the lowest. Refresher units typically have much lower stats than their peers simply because they can Sing or Dance.
I think the big problem for you is that you never mentioned using a bonus unit on your Arena team. Bonus units DOUBLE your score and are essential if you intend to rise Arena tiers. That is why it is usually a good idea to have a decent build on Alfonse, Sharena, and Anna because one of them is always a Bonus Unit. Additionally, every time your Bonus unit defeats an enemy, +3 is added to your score. While seemingly minor, this adds up over 5 matches and can lead to as much as 60 extra points added to your score, and every point counts when trying to break into the highest tiers.