Can I ask why you start with cauldron if abandon is your source?
Not entirely sure how you mean that.
"How am I getting an Abaddon Shard from Cauldron?" - Abaddon and Eden traded shards. It's plausible (if not anything like common) to pick up an Abaddon Shard through Eden.
Like how Contessa picked up PtV (
from Abaddon through Eden, unless I
completely misunderstood that part of the story - which, in a bit of fortuity, coincidentally also makes it appropriate that another Abaddon Shard 'fix' her,) in the first place.
"You don't have to deal with Cauldron if you're getting a Foreign Element Shard" - Absolutely. But the point is to have the most impact with the least setup possible, and Cauldron is far and away the most potent lever. I
want to be dealing with Cauldron.
(This is especially true given we're in the Golden Age - Above and beyond any other complications that aren't in play,
the Endbringers don't exist yet.
Avoid contact with Cauldron, and you're actively allowing one of the biggest problems leading to the state of the world in Gestation to come into being.
With the advance future knowledge that Endbringers exist and how they come about, an unblinded PtV should be able to either Path Eidolon to stop them from showing up them, to mitigate them, or to bring them in
on your side as best case.)
And doing it this way means I don't need to spend words on how I got the Shard, nor on getting in contact with Cauldron.
(I mean, sure, it's in the (unspoken) backstory, but (I think) the reader can fill it in well enough through implication.
It's nowhere near the level of "For Sale: Baby shoes. Never worn.", but I make no claims of being anything approaching a good author.

)
If you meant something else, I'll gladly clarify (or rethink).