Here's a more substantial kingdom that gives O(n^18) VP:

Artisan, Bank, Cellar, Cobbler, Counting House, Gardens, Ill-Gotten Gains, Masterpiece, Page, Vampire.

There are no +Buys, so we can only buy one card a turn. There's a chain of gainers, Artisan -> Vampire -> Cobbler. In n turns, we can have O(n) Artisans, O(n^2) Vampires, and O(n^3) Cobblers, and at least O(n^4) of any <=4 cost. None of these gainers can gain themselves or anything before them in the chain, so we won't have exponential growth.

With one Page, we can have Champion and so we don't need to worry about Actions. We can gain O(n^4) Pages, so we can also have O(n^4) Heros, letting us have at least O(n^5) of any treasures we desire. Also, using O(n^5) Ill-Gotten Gains, we can have O(n^6) Coppers. Our draw engine can use these Coppers with Counting House and Cellars. We can have O(n^4) Cellars and O(n^3) Counting Houses, so with O(n^3) Counting House/Copper pairs, we will be able to draw O(n^6)*O(n^3) cards in a turn (supposing we had that many cards). With O(n^5) Banks, we can get O(n^10) money, so we can overpay for Masterpiece to have O(n^9) silvers in our deck on our second to last turn. On our last turn, we can draw O(n^9) Silvers and O(n^5) Banks to hit O(n^14) money, overpaying for masterpiece.

Our final deck will have O(n^14) cards (mostly silvers) and O(n^4) Gardens, giving O(n^18) VP.