First off, I'd like to thank tim17 for this excellent puzzle. Here's my first take.

Kingdom: Stonemason, Village, Scrying Pool, Alchemist, Golem, Possession, Expand, Scheme, Fortress

Events: Seaway, Training, Lost Arts, Donate, Obelisk on Stonemason

Setup: Seaway, Training, and Lost Arts on Stonemason (so it gets +1 action, +1 coin, and +1 buy)

Victory points are simply generated by Obelisk.

Starting deck:

9 Scrying Pools

1 Scheme

1 Fortress

N Expands

N Stonemasons

At start of turn

play Scrying Pool, draw entire deck

play a Stonemason on the Fortress, gaining 2 Stonemasons

play Scheme to draw one Stonemason (and to allow us to topdeck a Scrying Pool for next turn)

Start of iteration

play all Stonemasons on Fortress, gaining 2 Stonemasons each time

play a Scrying Pool, drawing a lot of Stonemasons

play a Stonemason on Fortress, gain 2 Villages

play remaining Stonemasons on Fortress, gaining 2 Stonemasons each time

play a Scrying Pool, drawing a lot of Stonemasons and 2 Villages

play a Stonemason on Fortress, gain 2 Stonemasons

play 2 Villages, draw the two stonemasons

play Expand on a Scrying Pool, gain a Golem

play remaining Stonemasons on Fortress, gaining 2 Stonemasons each time

play a Scrying Pool, drawing a lot of Stonemasons and 1 Golem

play Expand on Golem, gain a Possession

play remaining Stonemasons on Fortress, gaining 2 Stonemasons each time

play a Scrying Pool, drawing a lot of Stonemasons and 1 Possession

play Stonemason on Possession, gain two Golems

play remaining Stonemasons on Fortress, gaining 2 Stonemasons each time

play a Scrying Pool, drawing a lot of Stonemasons and 2 Golems

play Stonemason on Golem, gain two Alchemists

play Stonemason on Golem, gain two Alchemists

play remaining Stonemasons on Fortress, gaining 2 Stonemasons each time

play a Scrying Pool, drawing a lot of Stonemasons and 4 Alchemists

play 4 Stonemasons on Alchemists, gain 8 Scrying Pools

play remaining Stonemasons on Fortress, gaining 2 Stonemasons each time

play a Scrying Pool, drawing a lot of Stonemasons and 8 Scrying Pools

End of iteration. This state matches the start of iteration state except we have about 128 times as many Stonemasons and 2 less Expands.

It may seem like an endless loop, but eventually we run out of Expands. Since neither Expands nor potion cards can be gained during a turn, the turn must eventually end. When the Expands run out, we keep performing the iterations just gaining and drawing Stonemasons until we are out of Scrying Pools and the action phase ends.

Buy phase

buy all of the Expands we can for next turn

topdeck a Scrying Pool (from playing Scheme)

Two Expands gives us 7 Scrying Pools, so if we start with N Expands, we do O(3.5*N) Scrying Pool passes that double the number of Stonemasons each time. That means we played O(N*2^(3.5*N)) Stonemasons for 1 buy each and 1 coin each. We can therefore buy O(N/7*2^(3.5*N)) Expands for the next turn. Our Stonemasons have increased by the same order. Therefore our growth rate is O(2^(3.5*N)) = O(11.31^N).