Accounts that I have at the bank all pay varying rates of interest. I usually donate the interest amounts to charity. Now, if I undertake a loan in which I pay an interest rate and only pay the interest amount due with the interest that I receive from my accounts (but pay the principle amount with my own earnings). Am I, in your opinion, in error?

I think that there is no harm in this dealing. The interest you are getting is not your right Islamically, while the interest you are paying is an injustice you are encountering. So, it is merely a situation of paying something that was not your right in order to pay off something that should not have been demanded from you in the first place.