Ignoring the infinite solutions, I think there's a solution that scales better than N^2. You can buy a bunch of Tunnels, followed by a bunch of Cursed Villages. Not sure how much you're allowed to stack hexes, but War should allow you to gain a bunch of gold (using Canal to skip past tunnels and Watchtower to trash Cursed Villages.) Then buy a bunch of triumphs. This doesn't sound very efficient, but it should scale as N^3, so with enough coffers it should eventually be better.

Here's how I think it looks so far.

Squire, Watchtower, Fortress, Tunnel, Catacombs, Cultist, Border Village, Changeling, Exorcist, Monastery.

Alms, Ball, Advance

Tomb

Each buy is proceeded with Travelling Fair, all buys (not trashed) will be topdecked, except Tunnels.

Buy Ball for Watchtower and Blessed Village, gain Sea's Gift, draw Watchtower

Buy Alms for Fortress, reveal Watchtower, trash it.

3 cards gained; 999,990 coins remaining.

We will now be purchasing Tunnels, Catacombs, Exorcists, and Monasteries.

Each with the same method for 2 coins each.

Play Advance on Fortress, gain Border Village and Catacombs. After resolving on-gain for Border Village, exchange it for a Changeling and trash with Watchtower.

Either keep Catacombs or reveal Watchtower, trash it, and gain one of {Tunnel, Exorcist, or Monastery}.

The process of gaining 1 Catacombs gains 3 cards total.

Gaining 1 Tunnel, Exorcist, or Monastery gains 4 cards each.

Now we have to draw all the Catacombs, Exorcists, and Monasteries into our hand.

Play Advance on Fortress, gain Border Village, Catacombs, and Changeling. Trash Catacombs, gain Squire. Trash Squire, gain Cultist. Trash Cultist, draw 3 cards. Trash Changeling.

This process for drawing 3 cards costs 2 coins and gains 5 cards.

Night Phase

Play Exorcist, trash Catacombs, gain Ghost, Gain Exorcist

Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw 2 Ghosts and an Exorcist.

1 Exorcist and 2 Catacombs are combined into 2 Ghosts, gaining a total of 5 cards in the process.

Play all Ghosts

Play all Monasteries, trashing Fortress

---- breaking down the numbers ----

Buying 166,654 Tunnels costs 333,308 coins and gains 666,616 cards.

Buying 41,666 Exorcists costs 83,332 coins and gains 166,614 cards.

Buying 83,330 Catacombs costs 166,660 coins and gains 249,990 cards.

Buying 125,009 Monasteries costs 250,018 coins and gains 500,036 cards.

Drawing 41,666 Exorcists + 83,330 Catacombs + 125,009 Monasteries takes 83,335 Cultists. Cost 166,670 coins gaining 416,675 cards.

We have exactly 2 coins left. Buy Travelling Fair, gain a Tunnel (as above) and then buy Triumph.

The Estate gave us a total of 1,999,936 gained cards. That's our score so far.

Night Phase

Combining our 41,666 Exorcists and 83,330 Catacombs into 83,330 Ghosts and drawing them gains another 208,325 cards.

Playing each Ghost gains another 166,655 Gold, which brings our total card gain to 13,889,361,086.

Playing each Monastery gains that many more VP, for a total score of 1.7362951e+15 VP.

We started with one million coins and effectively gained 1.7 billion VP per coin.

I want to thank everybody who helped get us this far. IMHO, collaboration is highly underrated in the real world.

And now that I'm all done with this analysis and have written it up, I just realized that Sewers would practically double the total VP.