It's been many years since I addressed the heat transfer capabilities of the refractory materials, so I don't recall much in the way of details. If memory serves, however, the maker generally provides technical data that includes the rate of transfer.
The only furnace I ever built with two layers was the one I showed, above. All others were single layer, and about three inches, just as you propose. That works fine, they just get hot on the outside. Applying an insulting layer there would be very acceptable, assuming it won't get abraded.
A couple things to think about. If you operate the furnace on top of a concrete pad, make sure you have adequate clearance between the bottom of the furnace and the floor. If you run long enough, you risk cracking the concrete from local expansion.
While some furnaces have been built that will melt cast iron, the end results are generally not very desirable. The prolonged heating cycle tends to burn off carbon, which destroys the desired qualities of the metal, but it can be done. The ability to achieve the desired temperature quickly is a definite advantage.
To be perfectly honest, I had no idea of a ratio of the discharge port versus furnace bore. When I built my first furnace, I had examined a McEngleven, and made some Kentucky windage adjustments, considering I had scaled it down for a #1 crucible (way too small for my eventual needs, so the next furnace was for a #8). All of my previous furnaces were fired by natural gas, and performed to my satisfaction. I could melt pure gold with no problems, which melts at a temperature very near that of copper. The temperature difference to melt cast iron, even one that is quite high in carbon, would be a substantial jump higher. I'm not convinced I could have enjoyed success. I make mention for reason. While I was more than satisfied with the performance of all of my creations, I may not have been had I hoped to melt iron. I believe, just as you do, that the design and heat transfer play a serious role in the degree of success one will achieve.
Like you, I had addressed the issue by starting to build a VERY small cupola. Only 4", which is reputed to be difficult to operate with success. I then encountered the opportunity to acquire a 50 kw induction furnace, so the cupola project was abandoned. The body was sold for scrap when I moved from Utah.
Thanks for your kind words. I try to share that which I have learned through the school of hard knocks. Some find it offensive.
Harold