Re: Alkyd paints for doors.
I've had good results with Sherwin-Williams Porch & Floor Enamel on doors. To get it to flow out smoothly I add some floetrol. I get a nice durable finish, though it's still not as hard as an oil-based paint, but if it's outside you won't have to worry about mildew problems since it's a water-based acrylic instead of oil-based.
If it's Inside, I'd agree with Sombreuil_mongrel about using a waterborne alkyd. I've never tried Ben Moore's Advanced but been curious to. My go to for interior doors and trim is Sherwin-Williams ProClassic waterborne alkyd. Dries nice and hard and flows out very smooth.