There's a small roof (about 6' wide by 4' deep) above my front door.
Rain and melting snow run off the front of the roof onto the stairs,
making them icy in the winter.

We got one estimate for about $600, because the contractor says we'd
have to rebuild the entire roof to change its slope. It currently is
a hip roof, and I think he wants to rebuild it to slope entirely to
the sides instead of to the front.

I'd prefer to just install a rain diverter strip. The websites that
describe them all show shingle roofs, but ours is a rubber membrane
roof with copper flashing at the edge. Is a rain diverter an option?

Jimmy