Here is just one idea for how to keep up with rosters for those who prefer to play out a current season to get a better feel for each team, as opposed to playing out an old season. I just set up for a series between the New York Mets and Milwaukee Brewers, so I use them as the example.
Periodically when I am about to start a new series, I open the depth chart for both teams, copy it with a ctrl+A then ctrl+C on each team's page in my series, and then copy both teams onto a spreadsheet to use to check the schedule. you will need to delete out a bunch of garbage rows, but end up with a sheet like this for two teams (except for the two rows at the bottom of each team that starts "On roster." and the extra narrow columns which you should insert).