A couple of considerations
I replicated your hyperbolic Hohmann calculation for Earth, and got 3.46 km/s. Close to your value.
But for the Venus part, the numbers seem off. Assuming a helocentric transfer orbit with apsis at the semi-major axis of Venus and Earth, and a circular orbit for venus, the relative velocity should be 2.71km/s, working out to a hyperbolic velocity of 10.63km/s at 6151km pericythe. Considering the pericythe velocity of a 6151km x 50,000km venus orbit is 9.70km/s, that's a delta-v requirement of only 0.93km/s.
The entire 3.46 km/s manoeuvre in Earth orbit is not required to be performed in a single burn. Doing a partial burn, you are still in an elliptical Earth orbit, and can wait some hours or days to get pack to perigee for the next part. A relatively short time compared to the interplanetary transfer. The "marginal" burn is a mere 0.28km/s on top of the escape velocity at the end, putting you into a non-looping hyperbolic escape trajectory. On the Venus side, the similar marginal single burn for capture is 0.35km/s. The rest can be done in increments.
A rule of thumb for escape trajectory burn times is to consider the radial acceleration in a rotating frame of reference:
$$a_{radial} = \omega^2r - \frac{\mu}{r^2}$$
While this is instantaneous of course, it's usable for upper bound calculations since the radial acceleration will only get lower as the distance grows.
At tangential escape velocity at 400km altitude, that's 8.7m/s² in a rotating reference frame. When looking at short periods of time, the altitude thus grows quadratically. Less than 15km for 1 minute, 60km for 2 minutes, 240km for 4 minutes. (Again, this is an upper bound. The actual altitude grows somewhat slower, so consider this an additional safety margin). From this, Steve Linton's estimate of a couple of minutes seems very reasonable. To get how much extra cost this adds, try doing your hyperbolic calculation for say 500km.
Getting the marginal cost of 0.28km/s done in a couple of minutes gives you acceleration requirements in the 1 - 5 m/s² range. As this marginal burn split up into parts is somewhat inconvenient, aiming for around a G of acceleration seems applicable.