Spins start from a stall. How deeply the airplane is stalled has an effect. How effective each surface is to cause that stall has an effect. How effective each surface is once in the stall and spin has an effect.

You say the inverted spin stops as expected. That would suggest the neutralized surfaces are not blanked by the airplane's attitude in that spin. And that they are in the other. You can't do much about the airflows since they're a result of the airplane's shape.

It could also be a problem with asymmetry, either in balance or shape. You probably don't want to try and reshape the airplane, so look a bit at the balance. Any chance the CG's vertical location is having an effect? It does in a highwing Cub for example. It's quite a bit below the wing and increases roll stability considerabley when the airplane is upright and decreases it when the airplane is inverted. That might be a cause in your situation. At least it's something that can be explored.