There is a similar process in sailing. With the tall masts, sometimes sailors can't get under bridges or overhangs. They have masts that "tabernacle" - that's the sailor's jargon for a mast that unhooks and drops down parallel to the surface of the water.
For the big masts, they have motorized winches that let them down and crank them up. For the smaller masts, you need a crew to unhook the guy wires and let the mast down.
In really small sailing dinghies, it's a one person job.
The trebuchet idea is creative, but I bet a simpler way could be found. You aren't raising it by remote control. Someone will be out there doing it. Maybe a concreted in pole sticking out of the ground one foot, with a hefty hinge attaching to the pole that holds the dish. Use a come-along to raise it up. Have it go up until it hits stops. Then hitch pin it into place.
Still sounds a lot more complicated than just leaving it up and painting a smile on it.