You can tinker with the lineups and usage settings. If you use "primary with rest" or "draft mode with rest" starting position players will be rested from time to time, with other players filling in for them. Sometimes this will force overusage of backup players. Also, you can try various combinations involving the major/minor settings -- the "40/25" method allows HAL to move players back and forth between the majors and minors, and creates a 40 man roster during September. Or you can try "minor leaguers ineligible" instead and set all low-usage players as inactive.
Another random factor is whether you use injuries or not. If you have three shortstops, let's say one has 430 atbats, one has 154 atbats, and one has 7 atbats -- if you use injuries, it is always possible for the two main shortstops to both be injured, forcing use of the third shortstop for several games even though he only has 7 atbats. One more idea: give individual batters with very few atbats the following settings: avoid lefties, avoid righties, bunt more, avoid using in blowouts, remove for def sub with lead -- in other words, do everything to keep them out of the game. Also, your third shortstop (to continue the hypothetical example) also comes in the game more often if the other shortstops are pinch-hit for. So you can set the other two shortstops with more atbats with both "don't PH for vs. lefties" and "don't PH for vs. righties."
However, especially if you are using drafted teams, there will always be some overusage and underusage. One other way to reduce overusage is to make rosters larger, and to make sure there are three or four players at every position