Gorgeous work Prashun!
I don't think the rails and dividers are chunky by any means, but one way to slim them down visually is to rabbet them and have a drawer front that overhangs the drawer. You can also set them back and just have drawer fronts visible.
I would not go slimmer than 3/4 for the stretcher, it counteracts a large force if you have weight on the center front of the desk (like someone sitting on it)