The thread you listed first in your first post contains a lot of discussion and detail on La Cl including some of the dangers.
Fine prefiltration is must,IMO and experience.
The precipitant evident in the clouding is harmful; it is known to clog breathing apparatuses . Some dose directly & get by. I personally, saw a yellow tang swim through a light cloud from a hobby commercial product and stop breathing in a friends tank , attempts to revive it immediately in new water were unsuccessful. I've also seen a 4 inch maxima calm get serious pinched mantle after exposure to a cloud; it died within a few days.
There are several ways it can go wrong:
LaCl disassociates in the water . The La binds with PO4;probably more readily with
PO4---, than PO4 species with a lesser charge. Comments from public aquarium folks suggest a max overall PO4 reduction floor at about .1+; I've seen it go to about .05 or so. So, when the PO4 is low the La will bind proportionately more CO3 instead: hence more alkalinity depletion.
Slow dosing to high water volume areas helps insure a maximum amount of PO4 in the water along with a maxmum amount of carbonate to pick up the slack lessening the amount of free La which will get through the filtration. The free lanthanum entering the tank may precipitate anywhere and the effects of the reaction may case trouble. Potential ingestion via drinking water with free or bound lanthanum or eating some may also cause trouble,speculatively speaking.
LaCl dosing can reduce PO4 very quickly leading to stress by organisms due to the rapid drop in available PO4.
As for dilution; I did the math before switching from a hobby grade product to Sea Klear years ago The SeaKlear was bout 1/10th the cost .
All in all, I chose not to stop using LaCl even with fine filtration and slow doing in favor of GFO which can be cost effective when regenerated. I do still use La CL outside the tank when curing rock leaching PO4.
I certainly can't explain the marketing claims about safety but IMO caveat emptor pertains.