I understand the potential unfairness of having to bowl on a 2nd shift and then having a make-up or a pre-bowl or post-bowl having clean, unused lanes during the day. They can score much better than a 2nd shift. Heck, it almost plain unfair to the opposing team that doesn't pre/post-bowl, not just the rest of the league, like your team for the high game award.
That said, the make-up/pre-bowl/post-bowl is part of the games that make up the league. The league or the USBC rules allow them. All the teams, including yours, must have agreed on the format and the reasons for allowing them. How can they not count for any and every award or anything else?
Unless there's a special league rule that says they do not count, I would say that they have to count. You can always work to get that changed for next year. I don't see how you can change it retroactively.
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"None are so blind as those who will not see."