Thanks for the reply!

I've gotten far enough into development where I wished I fixed this earlier rather than later. I definitely agree with the methodology in terms of taking the Mirror data from the ControlsScript. I was thinking it may be easier to load a Stance (Stance 2) with the P2 sprites, have a custom script read whether the character is on P1 side (1) or P2 side (-1) and then switch between the stance 1 and 2 accordingly. This would be the easiest solution in my mind(at least theoretically), however I'm having trouble finding how to code this.

This code is probably not right, but here's an example of what I'm thinking of.

public void CharacterOrientation
{
if (controlsScript.mirror == 1 && moveSetScript.currentCombatStance == CombatStances.Stance1)
    {
        controlsScript.stanceChange.casted = false;
    }

else if (controlsScript.mirror == 1 && moveSetScript.curentCombatStance == CombatStances.Stance2)
    {
        myMoveSetScript.ChangeMoveStances(stanceChange.Stance1);
        controlsScript.stanceChange.casted = true;
    }

else if (controlsScript.mirror == -1 && moveSetScript.curentCombatStance == CombatStances.Stance1)
    {
        myMoveSetScript.ChangeMoveStances(stanceChange.Stance2);
        controlsScript.stanceChange.casted = true;
    }
else
    {
        controlsScript.stanceChange.casted = false;
    }
    return;
}

Alternatively this may not even need a custom script, as it could (theoretically) be directly implemented into the MoveSetScript, making it a singular instance code where it just picks up on the character's stance and side of the stage, rather than having to go tell a custom script to look for specific sprites for each character.

Here's my example, although I'm not necessarily sure that void Awake is the correct place to put it. Right now it's only loading Stance1 for P1 and Stance2 for P2, not switching as I move one character to the other side. 

void Awake()
    {
        controlsScript = transform.parent.gameObject.GetComponent<ControlsScript>();
        hitBoxesScript = GetComponent<HitBoxesScript>();
        spriteRenderer = GetComponent<SpriteRenderer>();

        List<MoveSetData> loadedMoveSets = new List<MoveSetData>();
            foreach (MoveSetData moveSetData in controlsScript.myInfo.moves)
        {
            loadedMoveSets.Add(moveSetData);
        }
        foreach (string path in controlsScript.myInfo.stanceResourcePath)
        {
            loadedMoveSets.Add(Resources.Load<StanceInfo>(path).ConvertData());
        }
        controlsScript.loadedMoves = loadedMoveSets.ToArray();

        controlsScript.currentCombatStance = CombatStances.Stance10;
        ChangeMoveStances(CombatStances.Stance1);

        if (controlsScript.playerNum == 1)
        {
            if (controlsScript.mirror < 0)
                ChangeMoveStances(CombatStances.Stance2);
            else
                ChangeMoveStances(CombatStances.Stance1);
        }

        else
        {
            if (controlsScript.mirror > 0)
                ChangeMoveStances(CombatStances.Stance1);
            else
                ChangeMoveStances(CombatStances.Stance2);
        }

    }