Thanks for clarifying.
I think you're right to cut the Beacon text on the faction board - like you say, you don't really need it. I think just in the component manifest having the landmark labelled X1 Beacon landmark and adding the cards with X10 Will cards makes it nice and clear.
Ah, I didn't know the term 'activating' was already used in the Law. Although off the top of my head, I can't think of an instance of it on a faction board. If there's not one, I'd still plump for something like 'discard' as 'activating' a card in this case simply means discarding it (as I understand it). And to avoid confusion over cards in your hand, 'Craft by activating face up cards' would just change to 'Craft by discarding face up cards'.