Glad to hear the video got you thinking, that's really what it's all about. I struggled with making this one, because as you illustrate, there's a million ways to do it, and most of 'em will probably work. I'll address some of your specific questions, but first a comment on your last comment, regarding material sourcing and experimenting. On the last page of the half barrel thread GeorgeSr posted this link to using found clay to make rocket stove cores:http://www.rechoroket.com/Home_files/EnglishBook_1.pdf
I would highly encourage you to dig up some material from outside and experiment with that in a few configurations before purchasing exotic materials. You'll be surprised what you can do, even if you just dig up some mud from the yard. Don't agonize over the composition, just build a couple mud burn chambers and get a feel for the materials you have, and the way these things burn.
Okay, as for square vs. round, I couldn't tell you definitively, but I'd imagine not too much difference.
The plywood does need to come off, at some point once the whole thing is dry it will start getting hot there over time, not to mention the cob does an excellent job of binding the core together and sealing any problem areas. I believe it moves with the liner and is a part of a composite system. I wouldn't expect this core to hold up too very long without the outer cob shell. I could be wrong about that, I haven't tried it.
As for the solid/light weight issue, I think the inherent problem is trying to get anything that will hold the insulation there if the whole thing isn't solid. Any thin structure for the interior is going to need to go through heavy heat cycling and unless you engineer it just right it's going to eventually fail. This is just a simple way to hold a fairly large amount of insulation around the burn without getting too hung up on the system. It's easy to spin off the deep end and theorize about all sorts of exotic materials, believe me, I do it all the time. This way works fairly well for not too much cash or messing around. For sure there's other ways to do it, but this one really has no major downside that I've found. It is soft, but once you go through a couple patching sessions on the feed as use and wear dictate, it eventually stabilizes. I use a higher ration of fire cement in the patching and it creates a very hard shell where needed.
Lastly, the cardboard might work just fine. However, be aware that the clay holds a lot of moisture for a long time. You need to be able to burn the moisture out, and I would worry that the cardboard would be saturated and soft before the clay could support itself. It would probably work fine, but the hardibacker is really cheap and easy to work with. The whole board, of which I used about half for the interior mold, and another piece for the bottom to make moving the core easier, cost $10.
Good questions and good discussion, I'd love to see you build stuff and add to the knowledge base. I certainly don't think this is the very best way to do it, I just got so many requests for how I built my home system I wanted to share something. If you've read my build thread on the home system you'll know I made plenty of mistakes. I'd love to see a system come out of all this that was affordable, high performance, repeatable, and simple.