Interesting idea! I agree that the Civil War / Reconstruction era doesn’t really fit the pattern as well. The two popular vote / electoral vote mismatches of the era (1876, 1888) really were coinflip elections, and create a lot of the difference, such as the oddity of Cleveland’s non-consecutive term as well as the unusually long string of Republican victories.

It probably fits better to have McKinley as the start of the progressive era, with a double continuance of sorts-that also evens the two periods to 36 years.