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Scenario Idea: Saving President Lincoln
One of the most thoroughly documented leaders of recent years was President Lincoln. Historians know when he lived and exactly when and where he died. Wealthy members of the Republican Party have had the idea of rescuing him from assassination and bringing him to the present to endorse their next candidate for the presidency. While there is currently a Republican President, Theodore Roosevelt, he's refusing to back the idea or supply any help - while he has nothing against Lincoln, his stated position is that he doesn't wish to set a precedent that will lead to officially-sanctioned "retrieval" of people from the past, in contravention of America's laws against involuntary temporal transportation. He doesn't believe that Lincoln would come willingly. An unstated reason is that Roosevelt is also a little worried that the party might select Lincoln as its candidate at the next election if he proves unpopular, since there's nothing to stop either of them running for a third term of office.
Despite the lack of Presidential support the plan is going ahead, but to minimalise government interference will be mounted from a British ship. All of the Republicans involved have promised that Lincoln will only be brought to the present if he comes voluntarily.
The adventurers (who should be reasonably well-connected Britons) are asked to accompany the expedition as witnesses, to make sure that Lincoln is not coerced. At least one should be working for the British Secret Service, making sure (at the request of President Roosevelt) that the mission fails.