TransX, though easy for planning slingshots, isn't terribly accurate especially when it comes to slings of Jupiter. I've found that it tends to underestimate the slingshot effect that Jupiter has. To narrow down the flight to less dv used you could do a save when still sun centered stage but just before it switches to Jupiter centered stage. Then test rel inc at zero and Pe Ratio = 1. Do a run through to after it exits the jupiter centered stage and see how it did for the trip to saturn. Then do another test with the Pe Ratio =1.02 or something like that and see how it compared.
What I've wished would be available in TransX is that during the MCC as one is approaching jupiter for example, built into TransX, is a function that allows to utilize just the physics engine of Orbiter, and click an execute or integrate button that takes the current hypothetical maneuver you are setting up and it then does a test integration of what orbiter would end up being if this maneuver were done as planned. It should go fairly fast, maybe a couple of seconds, to integrate several months of flight. One then simply does a series of tests that might take less than a minute and it could save a lot of fuel in future MCCs. ??