I tried some of the strategies suggested above as Bryan (Stevenson as running mate, moderate or slightly left answers, no going to the West Coast).
It wasn't a fair trial, since I got both the Tammany Hall and the Hearst questions, and gave pro Tammany and pro Hearst answers.
Unfortunately, the game link URL did not work, so I can't link to the results or see how much better than I did with standard Bryan. Bryan carried the West Coast and New York, but lost Illinois, Indiana, and West Virginia by narrow margins, and probably would have gotten Illinois and Indiana at least, which had more EV than New York, without the Tammany Hall question. He also lost Maryland, Delaware, and North Dakota, all of which are winnable by Bryan in other situations. EV count was 236 to 211, and popular vote percentage was 51.2% for Bryan to 47;.6% for McKinley.