DH had an idea that I thought was genius! Unless there is something wrong with it that we haven't discovered yet!
He suggested asking our UK bank if we can put my dad on our account, and get him his own debit card. That way, dad in the US can take money out in dollars every month and deposit it into my US account in time for the direct debit.
Sunnyflower, I think Paypal charged me about £7 (which at the time was about $12) each of the times I have used it to send money to my dad. In comparison with other methods, I think its probably one of the cheapest way to do it, but still $12 a month on top of what I'm already paying adds up.