If I'm reading your post correctly, you're looking for a single-coil P-bass pickup (SCPB), not a split-coil humbucker?
Since you're looking for "authentic" tone and appearance, you may want to look into:
As I understand it, the original pickups had a fair amount of variance on the winding process: some were wound hot, some not as much. Each of the winders mentioned above have their own take on the pickup, and if you contact them, and do a little research, you'll find the one that fits for what you're looking for. Keep in mind, too, that the Duncan is an "off the shelf" pickup, meaning that they make what they make, with no input from you. Some of the other winders I referenced above will work with you and custom wind you the pickup, i.e. make it hotter or cooler, substitute magnet types, etc. There are lots of options with some of them.
Good luck, and have fun!
Originally Posted by Carl Jung
"The pendulum of the mind alternates between sense and nonsense, not between right and wrong."