Hi Firecat,
It sounds fine in theory, and I currently do the same things without the rewards (moving money to make payments), however the details that are now provided on your credit record would show that you have applied for credit, what type of account it is, if you are on a promotional offer, what level of overdraft facility you have.
As it is a credit account, they may not like you applying for two of them close together. You could state that you want one for paying your mortgage and the other for bills etc?
Good luck with it.
Sparky.