Closest approach

With a 109° angle and V_∞ 3864.1549 m/s, the 2L4 "closest approach" to Venus is 0.2290354646802355 / (3864.1549 * 3864.1549) * 3.24859E14. That is 4983 km. It's... better than Aldrin to Mars, at 4640 km over - rather into - Earth. Still, our girl has a 6050 km radius herself. Unless you are piloting the Pegasus from TNG I'd really not advise this. If it wasn't a ghost ship before . . .

Yeah, I knew it was going to be a "Powered Cycler", to be polite; nonballistic. So let's look at doi 10.2514/3.25519 to see what Aldrin, Byrnes, and Longuski did about it in 1993; back before S1L1 was a twinkle in the latter two's eyes.

For that 1L1 cycler, a relatively small maneuver of about 230 m/s performed at aphelion of the cycler orbit can rotate the argument of periapsis by an amount sufficient to make the flyby of Earth occur at 1000 km above the surface. What the three did was to look at the 15 (Earth) year cycle, which is 7 Mars years, to see what would happen to v_∞ and closest-approach both over at Earth and Mars on each flyby.

For us that would be 13 Venus years... 8 Earth. In our case 2L4 aphelion is, at first turn, where it is closest to Earth. It then hits aphelion thrice more before its journey down to perihelion, and up to Venus.

So what we do, I guess, is list all the maneuvres for a Synod A outbound in its four revolutions. Then the next four, and so on, until twenty are complete (equivalent to 20 Hohmann orbits: 10 synods, 16 Earth years &c.). Synod B likewise. Repeat for inbound.