I’d like to add the Permanent Mermaid LTR to all mermaid inactive sims in my world to keep them from turning back into humans, which seems to happen within a few days if they’re left to their own devices. However, MasterController -> Sim -> Basic -> Purchase Rewards seems to only allow adding rewards to my own currently selected sim - is there a way to add them for inactives?

I've been able to purchase rewards for inactives before, but I've only tried for previously played ones. The sims in your save might not have enough Lifetime Happiness points to buy any rewards. So try adding enough for the Permanent Mermaid LTR. The option is under MC > Sim > Intermediate > Lifetime Happiness.