Go. Drink. Enjoy the madness.
Although it won’t help you with your contest, there is a way to find help getting through Ulysses. The Teaching Company has a course called Joyce’s Ulysses by Professor James A. W. Heffernan. Listen to the excellent introduction. Then read the first chapter, listen to Heffernan’s lecture on it, and reread it. Repeat through all the chapters. It takes a good while, but if you aren’t in a graduate school with a Joyce specialist, it’s the best way to go.
Afterwards, if you are truly a brilliant masochist, have a go at Finnegans Wake, one of the most bought, least read books in history. It’s the only book like an acid trip I have ever read. :)