It turned out my maths were incomplete yesterday. I blame Longuski and McConaghy for not Showing Their Work. But with Aldrin's help I got "Vinf" and the angle at the beginning. Also of course we need trajectories that get close to Earth. TL;DR - the Venus / Earth cyclers are possible but (besides Hohmann 5S10) infeasible. With one intriguing exception, the 2L4.
There are no Right cyclers below 5S10, likewise 1P3+ and 2P7+ don't exist; and my calculator wasn't good for *P5 because it kept using Venus' own orbit for that (which doesn't intersect Earth's, duh). For the others, the best I got was 2L4 "left branch". Semimajor 0.841 earth AU; unpatched period 282 days (right branch was 244 - 2S4 - but it's terrible). Eccentricity 0.163; aphelion 0.979 AU. V∞ at Venus 3876.6 m/s. Turn angle at Venus 109 degrees. (Compare 5S10 rightbranch: 2705 m/s with no estimated turn angle.) All this assumes planar inclination and that the synods work like clocks. UPDATE 3/3: Fixed the clocks.
There should be a reverse cycler that gets from Earth to Venus about the same time. Then the thing goes around by itself until its two synods are up - bit more than three Earth years - and it is at Venus again. Also (as Hop David on the 5S10) since it is a 2P*, there will be two of these things on the move, so the other one can be boarded on the other synod.
Here's the bad news: the turn angles were frankly prohibitive for all the trajectories I looked at. For that I got none to blame but Lucifer his own dark self. The Venus / Earth Pentagram means the angles are in fifths rather than in Martian sevenths. Baseline 72 degrees, not 51.
Earth's perihelion is 0.98329 AU although, yes, the mutual ecliptic angles are a pain. In the best years of the 243 Earth/Venus cycle, I expect 2L4 will enter STL1 halo centred 0.0098 AU inward of that. There she can use the manifold for some deltaV help. But she can never use Earth's well directly and unassisted. I suppose sails are up on whatever revolutions are made after Earth.
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