"Last Thursdayism" is about as accurate as calling the Strategic Defence Initiative "Star Wars". If you were merely using it as shorthand, seeing as it is a quick, vernacular term, OK; but otherwise it looks like something between a sneer and propaganda.
"Random miracles unexplainable by science" is almost a tautology. IF you start from the point of view that miracles are the result of deliberate actions by a sentinent supernatural being, they are not *random*. They only look that way because they cannot be deterministically predicted, or even probabilistically predicted on the basis of past physical events and the current state of the system under study. (And if they *are* miracles, then science won't be able to explain them, by definition. Why you feel that means the word must be used as a perjorative is another matter...)
Cheers!
You completely missed or ducked my point. No matter. I know your game.