Jason, how exactly do cart permalinks result in an inventory issue?
By adding a hidden product (published_at to null) via a permalink I would have expected the "inventory issue" message to show. Not because there is an inventory issue - just because that's what message shows when you try and checkout with hidden items. I see this:
Which makes me ponder your comment about setting to null but still being able to add them.
The product variants can still be added to the cart if you know their ids or via cart permalinks.
How can you do it? Fully expect it to be me just being dumb at stupid oclock. (it is early am here)