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not trying to be a party pooper or anything, but if you want my honest answer, don't app for these cards, or don't even apply at all.
your amex has a really high balance as it is. if you're to apply for new lines of credit, and charge your honeymoon spending to it, there's a very good chance you will get FR and have your accounts closed.
the cards you're interested in also doesnt have a 0% APR promotional period. That means you're going to be hammered with interests fees once the 2nd statement arrives, and it's obvious you won't be able to pay it in full because you're already owing balances on your other cards. Also, the united card is a visa signature card; the minimum CL is 5000. There's almost zero chance Chase will approve you when you owe this much on your cards as it is, on top of the fact that none of your current CLs are near 5000.
Before you do anything, you really need to pay down your balances, especially your BCE balance. I'm not trying to sound mean or anything, especially right before you're going on a honeymoon. But I really do think you should at least pay down most (or all if possible) of your debt before you go on your honeymoon because you're just going to have more debt burden after your honeymoon.
have you considered getting a personal loan instead? It's not as "cool" as having a new shiny card and it doesn't have any lounge privileges or free checked bags, but at least the interest rates are much lower. Also, try checking out other cards with promotional 0% APR; the 0% APR should suit you pretty well for your current situation. It is hard to get approved for the "better" cards with your current utilization though so pay that down.
Edit: To add, once you pay down your debt, you should see your scores go up by quite a bit. I am guessing it should be around 700-750 range at the very least, or even higher, and a lot more cards will then be much easier to get approved for.
I'm with Enharu. You're best off waiting until you can pay the balances down more... Right now you're overall util is still pretty high so if you can pay more between now and your May closing dates that would probably be best.
I'm right there with you, waiting to app (although for different reasons) and I'm waiting to mid to late May when I'll have <10% util on 2 cards and <7% util overall to make sure my odds are at their highest. It's a pain, but it'll be worth it - I hope lol!
Enjoy your honeymoon
not a problem i'm glad if i can be of any help.
after you pay down your debt, try to see if you can get a CLI through Amex. After that, apply for the card(s) that you want and your chances will be a lot higher. Most banks like to match CLs or top your highest CL by a little, rather than to be the guinea pig themselves. this will take some time depending on how long you take it to pay it down + the time it takes for your balances to be reported to the CRAs. So if there's time constraints on your honeymoon trip, the best way to go about it is to get a consolidation / personal loan to pay off your current balances and then use your current cards for your honeymoon.
Best of luck!