Add a dice to the list of default dice:

Yellow: the Yellow dice has one face for each existing Monument. Rolling a Monument allows an Island to immediately once apply its effect, regardless of whether it is one-off or repeating. An Island may update the faces of their yellow dice to match the current list of existing momuments, in full, at any time.

Give each Island a yellow dice.

In the rule Generating New Monuments, change the fourth bullet point to read:

Roll a {X Land, X Foliage, X Animal Biomass, X * 10 Mana}, where X is half the land cost of the monument rounded up for repeating effects, or n times the land cost of the monument for one-off effects, where n is half the current round number. That is the effect of the monument