In the bad old days (early 90s) I used a patched conic solver.

I wager that there are tools to do that kicking around.

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Paths with a gravity assist (handy!)

https://www.mathworks.com/matlabcentral/fileexchange/39462-gravity-assist-trajectory-design-and-analysis?s_tid=blogs_rc_5

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Someone's thesis (Matlab, again)

https://repositories.lib.utexas.edu/handle/2152/ETD-UT-2011-12-4849

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More Matlab (just adjust Mars till Saturn)

https://github.com/chicomcastro/optimized-Earth-Mars-transfer

etc.

And there are half a dozen antique TDs about FORTRAN codes kicking around on the NASA TRS.