I edited the .ini files as shown in the videos linked here, but for some reason the title screen does not show up after I am knocked out in the intro section. I've noticed that it works for all the runs on the leaderboard, and I'm trying to figure out how to get it back so that my run can be considered legitimate (I'm assuming it would not be without that splash screen animation).

Did you change bNoForceMovies=False to true? If so Thats your issue. If not im not too sure, go through the video again and just check everything

Looks like I accidentally changed bNoForceMovies to true instead of bNoForceStartupMovies. That seems to have fixed it - thanks!