A cotton handling system is provided for a cotton harvesting machine with an onboard accumulator and a baling chamber. The cotton handling system includes meter, beater and feeder arrangements positioned downstream from one another for processing and conveying cotton from the accumulator to the baling chamber. A sequencing arrangement includes at least one mechanical sequencing device operatively coupled to the feeder arrangement and at least one of the meter and beater arrangements such that at least the feeder arrangement has a start-up activation time that is different from the meter and/or beater arrangements.