davebro "Most household paints these days are water based..."
No, dave, they're not. I am very rarely called upon to apply water based gloss.
And, even were that true, ("the paint has been there several weeks") the paint would by now have hardened so that an abrasive will be needed to shift it. A scraper fixed firmly to an extension pole to get the hardened outer surface of the paint off, then wire wool for the residue.
If there's a facing wall against which to rest the top of the ladder, Jack, do so (fold a towel over the top of the ladder to prevent it marking the facing wall), i will make things a tad easier.