i gotta agree, contracts are your best friend here. even some type of arrangement, an email, im / txt, anything. anything that reasonably outlines scope and you've got some ground to stand on.

outside initial business wheelings and dealings, what i normally do it send follow-up emails to whoever i'm working with just to re-stablish scope. for instance, i got a phone call last night about designing a landing page for an event. we talked technicalities, price, turnaround, all that jazz. what i'm going to do today is send a follow-up just reiterating what i agree to: i agree to do this work, for this much, by this date, so unless they see a discrepancy i will move forward as planned and anything further will be treated as a separate situation.

i'm with lowengard, ongoing billing is common. you get billed month-to-month for your TV, your phone, whatever other accounts you have, you don't get nailed with a 10k bill at the end of 4 years when you move. imo it's acceptable.

it depends on your relationship with your client, but reading your post, my first instinct was invoice for the initial scope, invoice for the out of scope work, refuse deliverables on anything outside of scope until all bills are settled. don't be an ******* about it and flat up hold things ransom like that, but this is where the phrase give an inch, take a mile comes from. they need to know scope has been broken and things outside of scope have to be dealt with separately, as such.