Are you sure you aren't looking at this backwards? Instead of looking for cards you CAN GET, why not look at cards you WANT or that would HELP YOU? If your eq will be clean in less than 2 months, it would be a shame to lose the opportunity to get cards you want because you applied for a bunch you could.
Yeah, GE pulls TU, but does having a card with little to no rewards and a high interest rate really help you? Sure, they "grow with you", but so does any bank (except maybe Cap1). The others just grow a little slower. And barclay's is pretty notorious for taking adverse action if you apply for a bunch of stuff in the 6 months AFTER you get their card. So if you want the priceline visa (2% cash back is pretty good), you should apply for that last, not first.
Is your EX going to remain with negatives for a while? If not, why not wait until all 3 are clean, then review your current cards and identify the gaps. At a minimum, you should have one card with a low interest rate (for emergencies and when you NEED to carry a balance short term), one with a good rewards structure (for most people, that means cash rewards with bonus categories that reflect their actual spending habits) and one with great customer service/customer support. Unless you spend a lot of money, getting more cards beyond a certain points just dilutes the value of the individual rewards programs. I love USAA as an institution, but every dollar I put on their card is a dollar I don't put on the CSP. If it comes time to use my UR points and I find myself a thousand short of my goal, I'll be pretty pissed that I spent money on other cards.
I know this board beats the idea of high limits for high limits sake to death. But grabbing a few good cards from a few good banks and using them responsibly WILL grow your limits. And they will be high limits on cards you actually use. In a little over a year, I've grown my limits from 1400 to a little over 60k without applying for a single GE card. With the exception of the USAA card, these are all cards I use monthly and they all serve a purpose beyond just having a high limit.
Focus on the long term, choose cards that help YOU achieve YOUR goals and resist the temptation to get cards just because you can.
In wallet: Ink Plus 10k, AMEX TE 25k. In bag: CSP 16k, USAA WMC 15k, Hyatt 13k, United MPE 12k, AMEX HHonors 3k. In SD: Cap 1 QS 5k, Discover IT 7k. FICO 08 says my EQ is now 844, was 510 in 2010.
