I just thought I would share because I think it's ridiculous that you can't change the billing date. I have changed the billing date on all my other bills to make it easier for me to budget for the month. It's really not that big of a deal though.
Why not auto bill your credit card?
I do that now, but I want to stop using my credit card. It's too tempting to put off paying it and I want to eliminate it. that's why I wanted to move the billing date so I don't put it on the CC any more.
I know its not optimal, but use a CC that you put in the drawer. Call that card and ask for an ACH payment setup against your checking account.
It would be DISH > CC > Bank, but at least you could pick your date.
It would also help with your credit score. Having routine activity (even minimal) will boost your score.