I got a response from customer support and they say I can trade in one item for one of equal or lesser value. I hope this means a burtgang can be exchanged for a conquerer if I provide the extra tokens. It says in their policy they won't accept additional currency to purchase an item of greater value :/

Please, if you think that Square Enix should change their policy on one time item restores so that you can purchase an item of greater value for additional currency, let me know. Maybe they'll consider it! I also don't think it's cool that a burtgang is cheaper than the other weapons because then this mess can happen :/