The thing is, the entire plan of saving the 1st literally hinges on the very fact of Minfilia's sacrifice at the end of ARR, and it comes (as I mentioned in OP) from lots of random factors. Apparently, no Minfilia caught in AOE = no Emissary, no averted calamity, etc. I'm trying to figure out the cause-effect, and whether it was as random as it seems. We can always assume it's just the storytelling convenience, but I'd rather believe that some inner logic and explanation still exists here.
Could it be that Urianger was, in fact, somehow aware of Minfilia's adventure long before WoL's Antitower tour? Long enough to figure out her place in this plan of his, maybe? Like, "Hey, look. We've got the right person for that Emissary job, and we could boost our Mother Crystal with powers? And we could annoy some Ascians, while we're at it? Let's make it happen! F*, Elibidius. Sorry, Ardbert."
True. And if I had to make an assumption, I'd say that it was Hydaelyn herself, who had guided Urianger and Minfilia both. First, she seized an opportunity to reach out and summon Minfilia's resources to her side. So that she could later reach out to Urianger ( either directly or via her Word of Mother), while WoL was busy with knights&dragons.* Hydaelyn seemed on the verge of failing altogether after the Antitower, so weakened that Minfilia was unable to hold her physical form after speaking to us. The rush of energy from the crystals allowed Minfilia to separate from Hydaelyn again and become an emissary rather than simply the Word of the Mother.
I've looked up the lore description of that WoD quest. the Archon confesses to having orchestrated events to grant Minfilia her freedom, that she might then use her newfound powers to prevent the First from being lost to the void. Though this revelation prompts outrage in your allies, she reassures them that she is happy to have been given such an opportunity. Not much of the specifics, I guess, but better than nothing..