I have Googled your suggested words "eudialyte metallurgy", to...

I have Googled your suggested words "eudialyte metallurgy", to see how ETM's eudialyte deposits might yield REEs.

I could find nothing describing the methods used in an actual commercial extraction plant, which is what ETM and Tanbreez are going to need. Neither company will have the money to experiment with commercialising the multiplicity of desktop laboratory attempts.

I could see no reference to a currently successful commercial extraction plant. Maybe a successful commercial extraction plant of REEs from eudialyte does exist, but it is playing its cards close to its chest, and has patented critical parts of their extraction process.

In the case of ETM and Tanbreez, which of the experimental desktop procedures would best suit commercialisation? Assuming of course that one of them could come up with the cash?