I have something I need to bind strong. Much stronger than super glue, but probably less than gorilla glue, although it's not bad if the bind is that strong. I need it to have a quick setting time, probably within a couple minutes. I need it to be removable by something less than a chisel. It doesn't matter if it's hard or rubbery, but it needs to come off pretty clean or close to it. Something like Sikaflex 227 (has a tensile strength of 245 psi, and tensile-sheer strength of 160 psi), although setting time of that is about an hour. I'm hoping to find something inside of 10 minute set time. Does any such adhesive exist?
If you need a glue glue, then cyanoacrylate may fill the bill. It's extremely strong (though has narrow tolerances for the mating surfaces, e.g. it can't bridge across gaps), and it removes with acetone. However, acetone can discolor or soften many surfaces.
If you are looking for a method to attach things to surfaces you can't afford to damage, then you should be using the higher tier of Gaffer tape. Gaffer tape is for temporary attachment of portable lighting in cinema/TV/ENG production, say you're interviewing the CEO in his office, but the room doesn't have nearly enough built-in lighting to shoot. So you need strong tape to secure some EyLights to his bookcase, and then, you need the tape to come off cleanly.
That's what gaffer tape does. That is its one job.