How about a cedar pergola that spans across the roof opening with columns on either side to cover the hard edge of the entry way wall & soffit area. You could stain the wood a grey or bluish transparent color or just leave it to weather to a natural grey. Make sure the columns are beefy enough so they don't look wimpy. Maybe 4 X 4's. You could add side trellises custom built to carry the horizontal lines (not the big box store type) to bring the eye out from the entrance into the stone wall. Train a clematis up the trellis planted within the stone wall or just leave it plain for a cleaner look. If this sounds too busy, how about just building a pergola across the existing roof line to connect the two sides and be done with it.

For the door- I could see a custom stile and rail door with a combination of panels and glass maintaining the same pitch or angle of the siding.