Yet another mind-boggeling thought: Maybe, Apollo 11 indeed did fail in the Star Trek Timeline and the Romulans altered history in a way that it actually resembles our timeline. Without the Eugenic Wars and World War Three, Zephram Cochrane would not have the reason to build the Phoenix in 2063.
That way, Players would actually need to sabotage Apollo 11. 
I love the thought of a prevailing USSR, though.