All the DPDT switches that I have seen have have 2 poles and 2 throws with off in the center. The two poles are independent. When the “toggle” is in the center neither of the four outer pins are connected to either of the commons The diagram you have drawn shows the lever in the center position acting on the top of pole 1 and the bottom of pole 2 which is not how an ON-OFF-ON DPDT switch works, so that conversion does not make sense since the base switch you are using is already an ON-ON-ON switch.
Can you point me to the wiring diagram for the switch shown.
However, if Digikey has the switch shown in your diagram in toggle, right angle PCB mounting format I would like to purchase some. SP3T toggle switches seem to be very rare.