OK, just to confirm I've understood, to wire the JST connector in parallel, does that mean I can simply wire the positive and negative terminals of the connector to the positive and negative contacts on the PCB (i.e. on top of the existing solder for the battery pack)?

thanks Alex. In case I go down that route, do you have any guidance on how to remove the existing battery pack? I can see the two soldered connectors but how/where else is the battery pack attached and what's the safest method of removal without damaging the board?