I'm not so strongly against an Alchemist over a Scrying Pool here. I'm not saying it's great, but it isn't terrible either.
Indeed getting herbalist for your first $2 would have helped you a lot.
But the more important thing is this: the game ends with eight single-province turns. It shouldn't.
The value of trashing depends a lot on the possibility to quickly add payload to a trimmed deck.
If you intend to go Royal Carriage on Count, the Alchemists aren't that good indeed. But both cost $5, that's expensive. You pay $10 for $6/turn.
I like the fool's golds as payload. Don't get them early, but add a couple (3?) when you start drawing the deck. They are a bit harder to draw, but $6 for $9/turn is an excellent rate.
This fool's gold plan should push you towards getting a second Amulet.
Don't be afraid you need points as soon as your opponent buys a Province. Piles aren't running out.