You choose
I absolutely would not apply for any more cards. Let's see a bunch of airline miles to use up in the short term or an interest rate bump over 15 or 30 years. Or even worse, denial of the loan. What would you choose?
Having refinanced starting in mid-September, 2010 and finally closing the loan in very late December, 2010, I can attest that the loan world has changed for the worse. They wanted documentation of every credit card, brokerage accounts, interest-earning accounts and 2 years of taxes (tried for a third year until I threatened the lender with some unpleasant things; I have been a customer of the lender's parent for over 40 years) and an explanation of every credit pull going back more than 6 months.
High FICO is not going to help you out with the process.
Once the loan closes, then it is ok to re-enter the fray.