Out of those 3 i've only had the DC, and it started at $1,200 and still sits at 1,200.
The secret seems to be, get approved for a crappy limit, and then take ANOTHER hp to get a CLI. I wasn't down with that so I lived with the $1,200. 
But that seemed to work for a lot of people.
@joedtx wrote:That does seem to be a unfortunate theme, they offer you a great promo but approve you for a small CL.
If it seems to good to be true... It usually is 
I got the Diamond Preferred at $1k in 2012. Made sense at the time, balances were higher and I was (still am) working down two closed accounts serviced by Citi.
Recently finally got a SP CLI link on the DP account, denied an actual CLI for too many recently opened accounts.
SM them asking if there were any BT offers, back two months ago or so. No. Then they sent me another BT offer a few weeks after that. This was the first BT offer after the initial 0% offer. But with the low limit, I'm just toying with them now.
Have you looked at BofA? They send me monthly BT offers on both cards, I imagine that occurs on other of their basic cards.
I'm not sure there is ever a guarantee of how to look at the initial limits given by Citi or BofA.
How much is the 0% balance you are trying to BT?
