Despite what everyone says, some of the biggest alligator gar are out in the winter time. You don't have much competition in terms of boats, so if you're willing to bundle up I would go in the winter. The water is typically clearer too.
I guided bowfishing on the texas coast for 6 years and late august and early september the gar are on the south shorelines schooling up to return to the rivers. 4ft to 8ft. Best time to find them easy.