DM's Call: Prestidigitation

[Dalebert]

It could be argued that the spell allows for a change in Target based upon the text which allows the spell to "color, clean, or soil items in a 1-foot cube each round," but this text does not make clear whether the area being cleaned actually moves, or if the spell only creates a fixed 1-foot cube "dishwasher" area

I think the description makes it very clear.

Once cast, a prestidigitation spell enables you to perform simple magical effects for 1 hour

It then goes on to give some examples and cleaning something in a 1 ft area is one of the examples of the various tricks you can do, once per round (presumably because you have to use an action each time), for an hour. Fortunately or unfortunately, depending on your POV, you have to make it happen with actions each round, but you can do that anywhere within range. And that's consistent with your interpretation that floating objects fall when you stop concentrating. So does the "dishwasher" effect.