I would go for something out of Silverado 99-07 or express van. U didn't say what u have with the 5.3 but 03 motor probably is DBW. So therefore u will need tac box and gas pedal. If u want heavy duty u probably want the 4L80E. It is physically bigger than 4L60E as well.
2003 5.3L was usually backed with a 4l60. Just putting another behind it would be the easiest. Or could upgrade with a harness and shift box to the 4l80. Just swapping engines without major modifications I would just go 4L60.