> That's before you get to the problem that space is ridiculously big, and sweeping it across the entirety of the surface of that imaginary sphere would probably take millions of years.

The scale isn't lost on me. I'm aware of how much ground would need to be covered when you get out that far, and I figured that might be a pretty damning factor. That said, you wouldn't need to sweep it across the entire surface, only enough of the surface to rule out any interfering debris between us and the object. Wouldn't take much. We would need VERY accurate models of the orbit based on effects on other bodies, but it's hard to totally rule it out in my head.