There are of course lots of questions. Such as what is the exact boiling point of cadmium iodide, how soluble is plutonium and uranium in liquid cadmium, and why they would be soluble but tungsten-molybdenum is not. Also as pressure increases, do the boiling points of cadmium metal and cadmium iodide diverge or converge? Also, what is the actual equilibrium temperature of a meltdown, it's most likely not 4000C vapor, but just molten metal, I would guess closer to 2000 Celsius is where the liquid density is low, the thermal radiation is high, all in equilibrium with the rate of internal energy production. I'm thinking here what temperature did the meltdown at Chernobyl and Fukushima attain. So even at 2000C a drop of liquid metal would fall through and boil the cadmium metal as it was falling, and create an insulating Leidenfrost layer as it falls, greatly reducing heat exchange cooling and ability to blend into the melt and dissolve away in the cadmium. There may be a need of a tungsten plate at the bottom, which is both dense in case it melts, but it does not melt at 2000C, and it would allow to cool the meltdown metal by boiling cadmium until it is able to dissolve in cadmium, if it does dissolve.
Also a steam explosion of cadmium iodide is not welcome, as explosions in a gas can be tolerated, but in a liquid they are devastating. That's how the Nazi dams were brought down, by underwater explosions. The only solution to it I can think of is a jacuzzi of cadmium iodide vapor being bubbled through the molten cadmium metal, which would be able to compress and liquefy and absorb shockwaves through the liquid, but creating and maintaining such a bubbling jacuzzi may be too complex, too much to ask for, via numerous tuyeres.
Oxides are a problem, as uranium and plutonium oxides have higher density than liquid cadmium near 11 g/cm3 vs 8 for cadmium metal. The cadmium amalgam of these metals cannot contact silicate as it may lead to oxide formation. So you would probably need a tungsten-molybdenum lining. The cadmium iodide vapor should be ok to contact polished granite walls of the chamber.
The leftovers after boiling cadmium iodide or cadmium metal should be soluble in HI/H2O, except lead, copper, silver, etc. Might need periodic nitric acid to dissolve the crud left over after distillation, and what vessels material to use for the distillation is a good material science problem.
Boron 10 control rods could be hanged from above if you are avoiding explosions anyway, and if the reactivity gets too high and the boiling too intense the liquid rises into the control rods, when the boiling quiesces it would drop below them. In case of an explosion the control rods would fall and float on top of the iodide, with specific gravity of 2.3, something that could be adjusted though by combining with a heavier metal as a boride, to sink inside the iodide but float on top of liquid cadmium. The boride would have to be of a metal more noble than cadmium, yet not dissolve out and be corroded by cadmium. In absence of control rods, the boiling itself is a negative void coefficient and should self regulate the reactivity somewhat, by increasing the fraction of neutrons lost to the environment due to lower density, and higher surface area, with some caveats, as follows:
A usual nuclear reactor is on the order of 1GW electric or 3GW thermal or so, with Chernobyl jumping to 30 GW power during the accident. Is there a way to have a large fast reactor, on the order of 100 GW continuous power? I believe in economies of scale, instead of spending billions per 3 GW thermal, it should be cheaper to build a large one, per GW. Part of the problem is that a critical mass is a critical mass, and you can only go so big on it. You could imagine a floating pool of metal cadmium, above which floats cadmium iodide dissolved uranium 235, 238 and plutonium 239 iodides, reacting. If you put many critical masses side by side, as a, say, 10x10 grid, or 100 total, if each individual one produces 3 GW of power by boiling cadmium iodide, 100 of them would be 300 GW. The neutron economy is improved too, because the losses to the environment are reduced, as one neutron lost from one critical mass section lands in the other, still useful, not lost, though here is the above caveat, that reactivity control becomes more difficult, as the void coefficient does not increase surface area and neutron loss to the environment, from increased boiling-bubbling, except around the perimeter of 100 grid sections. Then you would absolutely need the hanging boron control rods, as bubbling increases they get covered more. Also there is a danger of boiling off the coolant iodide completely, then the reacting mass would start boiling the metal cadmium beneath, possibly sitting on an insulating Leidenfrost cushion and reaching 2000C meltdown temperatures, decomposing the iodides van Arkel de Boer style, and sinking through the cadmium until it hits the tungsten plate, and sit there continuing to boil cadmium metal. There would need to be enough liquid cadmium to be able to absorb all the meltdown heat, yet not too much to over pressurize the chamber with 2000C cadmium vapor, though the pressure limits of a Geocore are extremely high. Under usual operation the 742C iodide may be under very low pressure and still generate an efficient steam pressure, because of its high temperature.
Yeah, lots of questions and issues, but if you design around the mishaps to begin with, and especially take everything underground with containment chambers, if both Chernobyl and Fukushima were underground with containment chambers carved into granite instead of containment buildings, we probably would not have heard about them much.
Also en.wikipedia.org/wiki/Uranium-233 under weapon material mentions a critical mass of 4-5 kg, less than the 8 to 10 kg I previously mentioned. This would make a total burnup be equivalent to 80-100 kiloton for a bomb based Geocore, but I'm afraid by the time you include enough fusion to generate enough energetic neutrons to fully destroy any leftover fissile material, you would most likely end up back at 200 kilotons minimum explosion size. One of these every 200 seconds would generate 4 terawatts thermal average with probably 1 terawatt electric obtainable from it. Dealing with borates to stop criticality of the leftovers is risky, but if it works that would require lots of recycling effort and cost of the leftovers, but a much smaller chamber size, probably a 10-20 kiloton bomb every 10-20 seconds, which would still be a 4 terawatt thermal reactor.