Regarding the Citi cards, I think I was also mentioned somewhere about the 6 month thing that Citi told me, but not always the case. Over the past two months I have closed a Citi Virgin Frlyer card and a City Qantas everyday card and just applied for the Citi Qantas Signature no problem.
Just on that Virgin/Qantas everyday history, I was also in possession of a Qantas Everyday card (and had been for a bit over 6 months) when I applied for the Virgin Flyer and had no issues. The only issue I ever had with Citi was when I had to Virgin Flyer card, closed it and applied for another 2 month later they gave me the bird - I had also just applied and received the Qantas card, but like I just mentioned, I waited another 6 months and the Virgin Money was mine again for the 3rd time without a hitch.