The Automatic cone wrenches are just a 7/8" or 3/4" open ends, nothing special. What you need (special) is the recessed lock nut wrench. They are easy to fabricate if you have a buddy with a lathe. Just use a piece of hex stock, drill a 3/8" hole through it, and mill the flats. You can purchase them on eBay for inflated prices. They are a MUST HAVE tool for any Bendix Automatic work.
People get confused about bearing adjustment because there's two different types of "adjustable" bearings in the world. Roller, or you might call them Timken bearings require a preload. The preload is very small and on an automobile wheel it's so small it's only measured in "inch pounds", there's no free play, no loose feeling.
On ball bearings, like we see on most bicycles, they require a very small amount of free play. The free play is to accommodate the poor machining and low quality fit. For example, if you're working on a Pro Road bike with a Campanolo Record or Shimano Dura-Ace group, they are so precise you will notice almost no perceived bearing play on their ball bearings. On a cheaply machined Bendix Two Speed you need enough free play adjusted into it to allow it to turn freely. Sorry, just the way it is. The rule is the least amount of free play that will still turn freely in the tightest position. It's exactly the way you already adjust your chain. You rotate the crank and check for tight spots caused by the out of round chainwheels. You want a very small amount of chain play in the tightest position, use the same rule on your hub bearing adjustment.
The reason they gave directions to rotate the sprocket, while turning in the adjusting cone in was because the adjusting cone has a sun gear machined onto it. You need to mesh the sun and the planet gears at the same time as you are turning in the adjusting cone. I'd bet you already discovered that as it won't go together unless you rotate the sprocket.
John