I’m not sure exactly how her power’s active component works. Does she keep stacking power every 18 hours and keep permanently doubling the valor costs of all recruitment forever onwards?
She doubles valor costs as long as she is in play but it is not cumulative. The valor cost will still be doubled if there are two of them in play rather than being doubled or tripled.
The force bonus she gets for settlements controlled by players replaces the prior bonus. So she will keep getting stronger as the players get more settlements but if you have the same number of settlements the queen well not just keep getting stronger. It is just the mechanism for how frequently the bonus recalculates or gets reapplied if you do something to remove it.
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Oh that’s a ton less scary than we expected. Thanks for the clarification! 
I’d like @IHG-BlightedPea to go through each of the bosses and be really clear about which boss powers are cumulative and which are not.