Highest Additional ATK/DEF on Crafted Equipments?

I've seen many Lil Empress Greatswords with 370+ ATK on CB, even 378... that's just insane, +34 from it's initial ATK (344) and sold for tens of millions despite of having no slot and not refined at all.

I wonder how high it can be (the +ATK/DEF) and how can I achieve that numbers? Well, at least close enough.
Getting less than +20 is already my best (My BS is 250 STR, 187 DEX and 137 Prof.)

 

Extra atk and def like slots is based on rng luck. How high it can go I'm uncertain of but the highest no slot you've seen were probably platinum anvil with no slots for the craft.

 

Become a member of the RNGeezus Cult and keep crafting equipments.

I'm guessing that the reason that they got those +34 atk on weapons anyway was due to them grinding for proficiency, and those are just one of the many lucky byproducts of their labor.

 

Thanks! If +ATK/DEF has nothing to do with Proficiency just like Slot does, then I won't hesitate to level my smith through Lil Empress series crafting. That way I can level my proficiency while having the chance to get a platinum craft at the same time. Even failed ones can cover the production cost, or almost.