I don't know racquetball, so I am not sure how long a cut throat game is likely to last. But if you could divide a class into 4 periods of about 10 minutes, then you have 6 courts times 4 periods which gives you 24 games, so it could be arranged that each student plays three periods with one bye period per class. Would that work? So each student would oppose 6 other students per 45 minute class, and over 4 meetings there is a some hope that they might oppose all other students at least once.
