Would there be a problem with just calling it something else other than science then? I don't see the need to bend definitions of words to account for inconvenient circumstances. I am a programmer and do hard stuff, I don't require people to call me a scientist. Mathematicians do hard stuff, they don't complain that they're not called scientists. Engineers, too, are not scientists. It's not pejorative, just a statement of fact. If what you say is correct, then what is the issue with just saying astronomy is not a scientific field?
Well attempting to exclude astronomy/astrophysics from the umbrella of science would be bending the definition far more than the current status quo.
Part of this is that science isn't about experimentation, it's about observation. We perform experiments when possible so that we have more stuff to observe, or more controlled events.
Much of astronomy, atmospheric physics, geology, medicine, the "soft" sciences and I'm sure plenty of other "hard" fields are at the mercy of certain phenomena having sweet FA for data points. And I'm sure they all do what astrophysicists do: make sure that what we do have plenty of data for works; make our extrapolations with as few assumptions/rounding errors as we can; and revisit existing models anytime we find a new data point.
It's as scientific as anything it's simply going to take longer to sort out in some cases.
I once had a very long and intense argument with a guy who was offended because I thought that I wasn't a scientist even though I studied Software Engineering (not even Computer Science).