Can you post a couple of pictures of this tractor? This is starting to get a little confusing and we need to get what it actually is nailed down before we can offer any real help. So far it sounds as though you have an 18hp Jim Dandy and you may if someone built it. If you have an 18hp kohler under the hood, you will have an odd shaped air filter cover and a little box housing the valves on top of the engine.
With the description of the rear wheels that you gave, you definetely have a 16xx tractor, not a 24.
They offered 1612, 1614, 1616, 1618, 2414, 2416 & 2418 models when the numbered series came into being.