I'm interested in this series, but I'm wondering how they'll explain away the gravity issue.
It really depends on the drive system. If you're using a simple rocket, then you have to stick to short burns and no "gravity" simply due to limitations on available reaction mass.
However, anyone planning a nontrivial trip around the system may have figured out a better system. And if you have the endurance to do extended burns, then the most reasonable course of action would be to accelerate continuously (at 1 gravity) for the first half of the trip, then flip around and decelerate (again at 1 gravity) for the second half. This leaves you with only a brief null-grav period.
Well, at least that would make sense in deep space. In an orbital system, you'd be much more biased towards acceleration for moving "outward", and much more biased towards deceleration for moving "inward".