Just thinking aloud:
1.there are cards which offer no interest till october eg discover; mbna had something where they would put cash from your credit card into your checking account (max $40 fee). Are there reward cards which will do something like this.
2. Are there reward debit cards which can be used to pay mortgage. Is the checking account somehow linked to debit reward card?
eg. use electronic check payment (debit card with same number as checking account?)
3. Balance transfer checks (from reward card) with no fee (you should have credit balance on your card so you are not charged interest).