From Fallen London Wiki (Staging)

The forgotten quarter thing it's talking about is the Sactuary of Crimson Petals, and the Shrine of Deep Blue Heaven, which is probably the easiest way of getting one of these, unless it's hallowmas. Unfortunately, it's only a 17% chance per Crimson petals, and a 12.5% Deep Blue.

Thanks to GreenShrike for doing the maths down there, I can confirm that Deep Blue has the cheapest action cost.