Ask for an end-of-year report. My secretary gives each bowler a packet at the end of the season that shows their games plotted on a graph, separate lines for the first, second, and third games. There's also a first, second, and third game average. It should be easy to just generate a list of scores.
As an aside, why does your team captain not keep the recap sheets each week? Those will have all the scores for your team.
SH