"The network is very slow - it's about following the Lagrange Points and using perturbation to go from A to B. Slight boosts, otherwise you might as well just go with a Hohmann transfer."

As I understand it, a Hohmann transfer to Venus, requires slowing down the solar orbital speed at Earth distance, so as to lower the perihelion to intersect Venus' orbital path.

Whereas I'm not sure exactly what pathway is used in "network" for planetary but I gather it mostly in the direction directly toward or away from the Sun.
If spacecraft can slowly go more or less directly to a planet in shortest distance, what is stopping it from going at faster speed?

"Counter-intuitively the delta-V between Earth and Venus is lowest when Earth is at aphelion, as that's when the Earth is moving slowest relative to the Sun."

Hm, do you know how much slower the Earth is moving relative to the Sun?

"But the synodic period for a particular point on one orbit to a particular point on another orbit can be a very long wait. Earth and Mars, for example, last came closest together - aside from the last few years - some 70,000 years ago. Earth-to-Venus might be a bit easier, but the wait time is still large."

But that's if it's a precise occurrence- such as, closest the Earth ever gets to Venus [most furthest]. Earth's aphelion or perihelion, of course, occurs every year and as far as synodic location it is about same each year- though it does have precession over longer period of time:
"The Earth reaches perihelion - the point in its orbit closest to the Sun - in early January, only about two weeks after the December solstice."
http://aa.usno.navy.mil/faq/docs/seasons_orbit.html

I don't know where Venus' aphelion or perihelion are relative to Earth's- but this doesn't matter much- it's a low eccentricity and it's changing could be as slow as Earth's.