To deal with Prospectors you have to understand how they work.
Prospectors only pop in on streets. Specifically the original gray streets (the ones with the sidewalks).
They are attracted to buildings, so they'll head for them. Then they disappear into the buildings, sometimes up to a minute.
They will sometimes just disappear without being next to a building. When that happens they'll reappear on a street.
When you have several running around some of them will become "linked", so when you tap one another will disappear and pop in at the spot where the one you just tapped was.
Prospectors are characters, so if you go into edit mode and turn off buildings, decorations, and plants you can see them better.
My strategy: I only have one strip of street. Everywhere else in town I have pavement or dirt for roads. I sit on that on section of street and new Prospectors pop in right on my screen. If I think I may have missed any I go to Krustyland or my Neighborhood and back, which forces the Prospectors to reappear on the street - which is right there beside my landing zone.
Oh, and it helps to send as many of your characters as possible on indoor tasks to get them out of the way.