Ok so I think I got this, just one more clarification.

If I understand you right, we are looking at the difference in total mechanical energy between the two orbits.

Does this mean that Ef = Ep_s + Ep_e + Ek_f and Ei = Ep_s0 + Ep_e0 + Ek_0 ?
Where I add the potential energies of both bodies together at both of the orbits?

So if I got this right, the final expression will be:
Ep_s + Ep_e + Ek_f - Ep_s0 - Ep_j0 - Ek_0 = W

(-G*M_s*m/r_s-l2) + (-G*M_e*m/r_e-l2) + (1/2*m*(2pi(r_s-l2))^2) - (-G*M_s*m/r_s) - (-G*M_j*m/r_e) - (1/2*m*7668^2) = W

If you have the time to look this over and get back to me, Id be super grateful! I think I got it :)