If you wanted a good faith discussion about potential ways of making nuclear acceptable, then maybe don't open with "as soon as they hear the word "nuclear", panic really hard and refuse to receive any new information that would actually address their concerns". All of your other comments have been fairly well indistinguishable from the standard gaslighting most advocates of mass expanding Gen III+ burner reactors spout.
If I take this definition of a 5, then reactor design (in the context of current fission concepts) is barely relevant, because the 5s start at the mine site (or in the case of breeders, in the reprocessing facility). Examples are Sellafield, La Hague, Kadapa, Serpent River, Rossing, Kakadu, Mayak and many others. One Fukushima is better than one La Hague. One chernobyl is preferable to a terawatt worth of La Hagues, Kadapas, and Sellafields.
At the other end there are unsustainable Kr-85 and other gaseous emissions during fuel handling for which there is no attempt at containment, fission product laden reprocessing effluent that is barely below safe thresholds for an entire continent's coast whilst only generating a few GW worth of fuel, long lived twice-cycled Pu240 and Pu241 for which there is no attempt at a clean reprocessing process, lost weapons grade plutonium, and (in the context of wantonly using as much energy as we please) waste heat cooking the planet directly.
Other 5s include at one end all small countries being locked into a small handful of fuel suppliers because plutonium separation and enrichment facilities are gatekept, or at the other end unlimited weapons proliferation.
Worth noting is in this context the current renewable industry has plenty of 5s but there are easier to see pathways to eliminating them (and many of them are eliminating themselves simply because highly polluting mines and slaves have a minimum cost marginally higher than abundant materials and full automation).
Some variation on a TRISO-style pellet based pebble bed reactor that somehow used natural uranium at high enough burnup that mining could be kept under control would be the vague shape of addressing as many of the 5s as possible. In this context there is still a near certainty of someone doing a Chevron and quietly dumping a few hundred tonnes of spent fuel somewhere it would begin leaking and be impossible to clean up in a few decades, as well as cumulative low level medium lived radioactive emissions with a similar risk profile (although different mechanisms and harms) to CO2 or methane emissions (ie. Harmless at low levels but terrible in aggregate).
It's difficult to imagine a scenario where the number of 5s in a fission reactor is preferable to the alternatives. You'd need a breeder that could take U238/Th232 and breed/burn all of the Am,Cm,Np,Pu until only fission products were left as well as some way of vitrifying all of the fission products including tritium and noble gases on site with no effluent whilst never having a weapons grade fissile/fertile ratio in any of the weaponisable elements. Even then there would probably be one or two quite nasty long alpha decay chains with at least one medium lived step due to the number of opportunities for transmutation.
Even if that last were solved, it's still inferior to solar for building a civilisation on due to waste heat.
Such a device is also far more scifi than an anuetronic direct conversion He3 fusion reactor which also solves that last to about the same extent solar can (but has a more difficult pathway to being built from abundant materials).