Pat, in thinking this through, I'd have to say that the best overall solution might be topping the outer ledge of the sills with HardiPlank lap siding. This is a cement impregnated siding product available smooth or wood-grained, which holds paint really well and is very weather-resistant.
The catch here is that the outer ledge would need to be at least 5/16" lower than the inner ledge to accomodate the thick ness without creating a dam for water. Most ledges are about 1/2" lower, so this is likely to work.
The toughest part would be cutting the siding into notched strips to fit the sills, and smothing the exposed cut ends. I'd adhere them to the sills with a flexible caulking, no nails; this will mean no chance for water to seep through nail holes, and easier removal should you later wish to take them off.