I have a couple of ideas regarding the cage.
1. Get a sheet of sturdy impact resistant polycarbonate and heat bend it into an open sided guard that covers the skylight front and back. Alternatively, it could be fit to a frame.
2. Make a cage out of stainless steel mesh. There's a lot available with different sized meshes and wire gauges but this might get expensive. It's often only available in large rolls.
3. Make something out of a suitably sized SSS BBQ grill grate. This might be cheaper and would be tougher than the mesh:
https://www.amazon.com/stainless-ste...el+grill+grate
3. It wouldn't help with dropping branches, but a simple guard in front of the skylight might, when driving, deflect branches upward long enough for the skylight to pass under. Even at 10 MPH, it would be a very short time. An angled BBQ grate that slants partially over the skylight should be pretty effective and relatively inexpensive.
I won't be going on my roof for a while due to some current physical limitations so I won't be trying this anytime soon.