I think you can get CLI's (and some decent CC's) with a BK reporting. However, you will NOT get them as quickly or with as high of limits as a person with no BK reporting. My BK recently dropped off, and some cards I never could get with the BK reporting. I was able to get some decent limits (5-10k) but this was when my score was in the 680-710 range, with some age on the cards. I was recently denied a CLI from Citi, for a six month old card for having too many new accounts. 

Stories abound on the boards (if you read closely) of people with much better credit profiles than yours (sorry, just being honest) being denied CLIs and CC's. you seem to be looking for CLI's without properly aging your accounts. It is NOT unusual for Barclays to only give CLI's every 6 months, and it is NOT unusual for them to refuse a second card to a person with another account with them (this is what you wrote about another to thread). It is not unusual for Citi to not grant CLI's immediately unsure recently unsecured account. 

I got AMEX accts while my BK was reporting, and although they gave me the cards, I was denied CLI's 3 times, du. To the BK being on my record. I just waited them out. 

Chill out, you are trying to do too much too fast, which clearly is a red flag, as your BK is not all that old, and your score has not rebounded sufficiently. You are on the cusp of exhibiting "credit seeking behavior" which apparently your CC issuers do not like.