I think your first option is closer to the mark Colwyn. Exchange companies tend to have a pretty good idea of what currencies are in demand and which ones aren't, on daily or even hourly basis. I don't think they keep a large "stock" as such, but buy sufficient currency to meet their projected demand, again within a very short time frame.
Maybe now the holiday season is almost with us we'll see a slight loosening of the TCB's fiscal policy of hoovering up Lira from most of the FX markets.
Anyway, a stronger lira suits me just now... we're in the process of selling our house in Istanbul and it's being sold in Lira
JF