I liked Haddock's wording for it. It's both precise and concise:
When you shuffle this, put this anywhere among the shuffled cards.
Note that this does not make Stash function like it used to (letting you see the cards not being shuffled), or make it cease to matter if your draw-4 was 2+2 or what.
And, uh, I guess you can't answer anything about this, so I'll just wonder aloud. You mentioned reprinting Stash and it makes me wonder in what form we might see promo cards reprinted. Or maybe you already said and I missed it.
Currently there are no plans to change how English promos are distributed; RGG gives them to BGG to support BGG, and BGG sells them (and then sometimes they're available other ways briefly, and foreign publishers have a lot of leeway in terms of how they give theirs out). RGG doesn't want to e.g. sell a box of promos, because then he'd no longer be supporting BGG with them. For all I know that may change someday, but it has not changed yet.
They get printed up as "needed." Apparently Black Market is sold out so that one might be first to get a new printing. I don't know when that stuff will happen though, or if Black Market is actually next in line or what (after the new one). One day, and it will be a surprise, I will find out that now some subset of the new images are being made and I will proofread them and all that. Black Market will be a lot better-phrased, saying you can play treasures and stuff. Envoy won't say "draw." You know. Whatever good improvements, like any expansion getting this treatment. And so Stash, it will get a new wording too, trying to be a good one.
As it stands that wording is similar to Haddock's, meaning it does not preserve the ability to peek at those cards, meaning it in turn creates rules questions for certain card-drawers.