Is it possible to use the RTS pin as DTR?
All RS232 pins are electrically identical. The MAX3232 device does level conversion on two pairs of lines but it can handle any of the lines.

The one thing to be careful about with the board shown is that if you switch lines on the logic-level (solder pad) side, you will end up with the signal on thw wrong pin of the DB9. You will need to modify the device on the other end of the cable or modify the cable.