After careful consideration and sourcing what was within my reach, I've got a plan now.
The original (really nasty, totally NOT airtight) box stove here was liberated as I got a great deal on a much safer airtight stove.
The 'new' stove will be used for burning the big chunks of cordwood here as needed - despite it's ridiculous location way at the front of the apartment where little heat is needed at all.
I've stripped down the nasty old stove to just a sort of flat base with it's legs attached.
It was literally bolted together and all the extra cast iron left over will make some dandy thermal mass.
I will re-use that base & legs to boost the burn tunnel off of the old wooden floor - so the 1st problem is now solved !!
The potter I got the bricks from also gave me a small, old kiln, which has nicely banded top & bottom parts of stainless steel & firebrick, and I aim to re-use these under the riser and at the top of the 1st barrel, most likely.
I remain uncertain as to what I can use the kiln's body for as it is just around 14" tall, so I may dismantle it and re-use it's bricks.
This is where the project stands presently - before I can actually start the build I need to partially dismantle and move a monster side-by-side 'frig through a bit of an obstacle course (it literally will NOT fit through the mud room's inside door !!!) so it must go down & up some steps to arrive in the actual kitchen minus it's doors.
Once I've cleared that space I shall start getting photos of all this stuff and I will post them for others to see here.
Thanks Folks - for the guidance in all of this, it is greatly appreciated !!!