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[Deadlock39]

Use Villages from the Black Market instead of Shanty Town (there are at least 9) Change the Bane to Loan, and put in Farmland for 1 more Silver.

I think you can also play 1 Highway from the Black Market, which allows you to use Workshop and Ironworks from the Black Market to gain the last Horn of Plenty and IGG, then use Develop to trash a $5 from the Black Market and gain a Hoard (and a Trader), and use University (one of your BM Villages) to gain the last Haggler.  There are more details to work out with playing the Villages, having your Deck stacked perfectly, and possibly using a +cards or two to pick up your gained cards, but I don't think there are any reasons why it wouldn't work with perfect shuffling.

[jimjam]

Apprentice is good but takes up a kingdom slot; cellar/counting house is terminal and dumps a bunch of copper into your discard (unless you want to play two counting houses). Black Market Native Village, however, is the correct drawer.

[jotheonah]

Are we intentionally ignoring the Possession-Embargo-Trader trick? Because then the answer is infinity.

[Deadlock39]

Are we intentionally ignoring the Possession-Embargo-Trader trick? Because then the answer is infinity.

Yes we are.

From the OP:

(theoretically, this can be infinitely high if Embargo was trashed on a Possession turn, but let's ignore Possession like in all puzzles)

[jotheonah]

My bad. Speedread right past it evidently...

[Voltgloss]

Native Village is a brilliant idea.  Though I don't envy anyone the "fun" of putting 60+ cards on a Native Village mat with only one Native Village in their deck. 

Are we limiting the size of the Black Market deck at all?

[Deadlock39]

Are we limiting the size of the Black Market deck at all?

Puzzles usually don't since the literal wording on the card allows for it to contain every single card not in the Kingdom.  Isotropic is technically a variant (but I also thing the Card FAQ indicates you can choose the cards any way you would like)