No amount of gil sinks is going to keep up with the current inflow of gil without the gil sinks being crazy and making the game suck for newer players. You need to look at it the other way too. There's too much gil flowing into the economy. Leves and NPCed items are the main sources.
They should get rid of gil rewards on most * leves and make them rewarding in another way. Reward the leves with items which have value and can be sold to players if someone does want gil. Shards and crystals would make perfect rewards. Everyone is always complaining about the price of them anyway.
* Keep gil rewards for leves of ranks 1, 10 and 20 so that new players can still earn some starter gil. However since they'll want shards and crystals too make the reward random between the two.
So I've just taken about 200 million extra gil per day out of the economy with a simple change.
Next, get rid of the huge inflow of cash from NPCed items. Cut everything given for items by 2/3s.
There goes tens of millions more new gil from entering the economy each day.