Clue to me is in where you said your cable works perfectly with your Leonardo and Millenium ECU's - Those ECU's will have the 8 pin (only a few pins used) Molex type connector as opposed to the later AEB type 4 pin Supaseal connector. Tartarini systems that use the Molex connector have a different pinout on the connector (some of the pins on the second row are used as opposed to other AEB systems that use pins all on the same row).
Your cable will work if you just chop into 2 wires on your interface (the wires that are not connected by the Molex connection) and the relative same wires on your LPG system's interface connector cable - just make a temporary patch using bits of wire to make the connections that your Molex connection isn't making. You should be able to compare wire colours to your Leonardo / Millenium system. Or instead of messing with USB to serial dongles, chopping into wiring or buying a cheap supposedly Tartarini specific cable you might prefer to buy a proper AEB USB to Supaseal cable and a AEB Supaseal to Molex interface adaptor. The Molex connector on the adaptor is wired for both normal AEB type Molex connectors and Tartarini type Molex connectors.