Off-the-box WordPress is good, but sometimes you need to unlock its full power.
In this case, you cannot use WordPress.com, but you can use WPEngine instead.
With WPEngine, you can ask a WordPress developer to do advanced things for you such as define specialised posts type, with advanced custom fields and your own design.
WordPress developers are not rare, they identify themselves as such or sometimes as PHP developers. In both cases, these people can do really advanced things for you at a reasonable price.