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I've done a bit of digging. You can set the max number of iterations and the tolerance.

minimize(F, [4,3,2,1], algorithm='ncg', avextol=10^(-30) , maxiter =10000 )

These get passed to scipy. However, this does not resolve your issue.

I agree with your symbolic approach! Here a different way to code it:

soln=solve(list(F.gradient()),[x,y,z,L])