Personally I think your microwave is bad. A huge clue is that it takes 28 seconds before the trip. That's quite a while and sort of rules out any surge currents or instantaneous anomolies. It could be that the magnetron in the microwave heats up at about that point and starts drawing much more power. A partially shorted winding will do this when hot, the magnetron would keep running but at a much higher current.
To make a current measuring jig on the cheap: Take a short extension cord and cut about a foot of the sheathing off without cutting the inside wires. Next cut just the black wire in the center of the exposed section. Connect a current meter between the black wires. Tape everything up so you don't get electrocuted. Plug the microwave into the extension cord and then the extension cord into the outlet. Heat a cup of water and read the current, see if it starts to creep upwards as it goes along, maybe even spiking just as it trips.