I think the best Gil sink we already have are the market board taxes, because they are dynamic. When the Gil loses value the prices go higher and because of the percentage nature of the taxes more Gil gets removed from the game. But the taxes are not high enough and should be increased.

However, the economy and the value of Gil is completely broken anyway, thanks to the bots I guess. Stuff you can freely craft and gather does not get more expensive. Gear and food and everything is still mostly at the same price since HW, despite that more Gil is in the game. But everything wich only drops randomly gets more and more expensive, like the hairstlye from Delubrum.
This means working for your Gil gets harder, up to the point where it does not make sense anymore to spend the time to craft and gather.

Tackling the bots wich are flooding the market and automatically undercut the prices goes hand in hand with increasing the value of Gil. Then prices for everyday crafts will go up but so goes the money you will get when you are selling something and the disparity between gathered and crafted and randomlly dropped items should go down.