I tend to sim day by day and I don't play out the games. I check the boxscores of the league after every day and check the news stories for interesting events. It's a little slower but it's fast enough where I can usually finish half a season in an evening. I also get a nice connection with the players and the other teams in my division. Currently I'm working on preparing my Scandinavian League for OOTP6 when it comes out.
When I create my fictional leagues, I pick a team to GM and stick with them for the duration of the league. I like to see how the team's history develops, which players were longtime members of the team who might not be outstanding but played hard, stars and goats and who the greatest rivals are, both other teams and players. I get attached to players like Demetrio Lamos who went from mop-up man to All-Star starting pitcher. I learn to hate the other pitchers in my division that always seem to win against me. I guess I sort of play as both GM and Ultimate Fan