The cost of the seat is removed from the prizepool.
How do you do this?
Sounds like maybe what you need is the ability to enter a prize description "override". In other words, you want to be able to create a prize that is either a fixed amount or a percentage of the pot, but instead of displaying the amount you'd rather display some sort of description for it ... right?
On the Prizes tab, you would see that it is a "Fixed" prize (for example), and its amount, but on the Game window you would see some text you've entered instead of the prize amount.
Does that sound right?