Internal surface area, yes. Only walls and roof above the height of the exit flue are counted in this.
Here is a good description of an adjustable plunger tube (they can be non-adjustable also, where the adjustment feature is not needed). Putting the sliding part inside the fixed part would allow the moving joint to be inside the bell and only a fixed pipe going through the bell roof. It may be tricky for you to do this, unless you can put a cleanout/access point in the base of the bell to reach the tube for adjustment. You should have a cleanout somewhere in the bottom side of the bell to pull fly ash buildup every few years.
I would move the feed opening farther from the wall, as that might in extreme circumstances have flames coming back out the top. It should not happen with a well built RMH, but better safe than sorry. You could probably twist the core so there is enough space behind the feed tube for exhaust gases to freely reach the exit. 4" clear would probably work fine in your case. Your core's floor would only be 16" below cabin floor level, and even accounting for 4-5" of burn tunnel floor thickness there would be around a foot of clearance below that floor. You can build piers to support the core and allow free airflow beneath it as well as some around the sides.
A 4" thick cob jacket behind the barrel (say a half cylinder an inch clear of the barrel and 8" taller) would protect the wall whether the LSC is technically "non-combustible" or not, and would allow easy barrel removal. A barrel with a lid can be placed with the solid floor largely cut out and the lid on top, so inspection is a very simple matter. Then the barrel does not need to be removable.
How thick are you planning to make the bell walls? I would expect your 7" burn tunnel floor to be about 24" long, plus a few all around for brick thickness. Maybe 30-32" long overall. How wide do you expect the bell interior to be? 3'-6" outside with 4" walls would leave 34" - workable if the core is square with the bell and pushed against one side. Or you could turn the core about 45 degrees with the feed out into the room (4" clear of the bell wall) and the exhaust behind it. With a good cob jacket behind the barrel and some airspace to the wall, you should be safe and convenient. You would obviously want the exhaust to rise straight from the bell interior for the adjustable plunger tube.
If you need to shift the exhaust at the roof to clear a rafter, I would suggest putting one or two lengths of stovepipe at a slight angle rather than a pair of 45 degree fittings. It's a good thing RMHs don't leave creosote, as I would not want to get on that roof peak in winter to sweep it