I like the distinction between mocking new code and mocking legacy code. But I think both tools support both styles, so this is no reason to switch around the mocking tool.
For mockito: Mockito.verifyNoMoreInteractions(mocks)
This enforces that no accidental interactions at the same time as you get to put the verifications where they logically belong: With the other assertions.
I would wager that JMock has a converse setting, where you can turn off extra validations.