Have you considered stopping by a branch or calling Chase and seeing if you can BT the two cards you have to a slate card? Applying online with two cards maxed out is surely going to result in a 7-10 message or a flat our denial. If you cant stop by a branch, call and apply. If you are declined ask to speak to an underwriter for a reconsideration and fully explain the situation to them. In this case honesty is probably the best policy and could result in you being able to successfully get a card. Blindly applying for lots of BT cards online is doing nothing but racking up inquiries and makes you look desperate, which you will have to explain if Chase declines you initially and you end up speaking with an underwriter.
Whatever you do, if you end up getting everything BT'd over don't make the mistake of running up the cards back to their limits again. You might of just gotten a new job with a huge career opportunity, but there are tons of us that were in similar situations in our younger twenties and ended up spending the majority of our late twenties and early thirties digging ourselves out of the hole we put ourselves in