Do you have any open loans? If not, I'd seriously consider implementing the SSL technique before you do anything else.
http://ficoforums.myfico.com/t5/Understanding-FICO-Scoring/Adding-an-installment-loan-the-Share-Secu...
That should get you (roughly) 30 more points, which should help with the applications.
As others have suggested, wait until you have 13 months of credit history before applying for any more cards.
A perfectly reasonable compromise might be to apply for three cards in your first spree, then garden for 13 more months, then apply for three more.
Do be sure to have done some research on Chase cards first. Apply for any you really love (e.g. the no annual fee Freedom with its 5% quarterly categories) before you apply for any other.
Tend to prefer no annual fee cards -- cards with AFs are in my judgment rarely worth it. There's the rare exception (e.g. the Amex BCP for someone with a big family who buys $6000+ worth of groceries every year) but in general AF cards cost you money in the long run.
