FIXED Update: I switched the two electrical connections on the main hydraulic cylinder and then ran the top through 3 complete manual cycles. Hooked up the battery and tried putting the top down with the car running. Windows went down when the handle was turned, and the top cycled down without any issue other than a little whining from air in the hydraulic lines. Put the top back up without issue as well. So, success! Rookie mistake on my part. Note to self: always label or take pictures before taking things apart.