If you just want to add more mileage to the MAN-EWR-PTY, change the routing to MAN-EWR-IAH-PTY. This is a valid routing and will add 970 EQM each way. You can also route MAN-EWR-MSY-IAH-PTY which will give you 1470 additional EQM each way. Neither of the MAN-EWR flights get you into EWR early enough to complete the trip to PTY on the same day with all of the connections. There's also MAN-EWR-MSY-IAH-MCO-PTY (another 420 EQM) and MAN-EWR-MSY-IAH-MIA-PTY another (424 EQM) which are valid routings. THere's even MAN-EWR-MSY-IAH-LAX-PTY another (3875 EQM).
Maybe someone with more knowledge can comment about what the fare rules would say about an overnight in MSY or IAH since the schedule would allow this. You might also ask the 'pros' in the MR forum about rhese specific routings and how to handle fares and overnights.