Would it be possible for there to be an almost torchship (essentially a very, very weak one) which could fly almost brachistochrone trajectories? So instead of a full on brachistochrone, where you burn straight for the target planet then flip half way and decelerate, an almost-brachistochrone where you burn for a bit towards the planet then spend some time on the float before decelerating.
It appears to me that by "brachistochrone" you mean a least-time trajectory, i.e., the trajectory which given the delta-v the ship is capable of, is the shortest transit time path.
If you have a ship that accelerates at 1g to the half-way point and then flips over and decelerates at 1g, Mars is 2-5 days away (depending on the relative positions of Mars and Earth) and you can pretty well ignore the orbital velocities of the planets and just "head for Mars".
If the ship is capable of 1g for less time -- say just a day, total, then you accelerate towards Mars for a half-day, coast at around 400 kps, and then a half-day out from Mars, decelerate back down to zero velocity. This would be a much slower trip? Not that much slower -- the coast time would typically be in the 5-10 day range. (Planetary movement is still barely worth worrying about.)
If you 'only' have the capability of 2 hours of 1 g acceleration (1 hour at the start and another hour at the end), you hit a top velocity of around 35 kps, and the coast time is now maybe 50 days, and you need to take orbital motions carefully into account.
Bring the available acceleration time down another factor of ten and you pretty much have an ordinary chemical rocket!
There is a family of shortest time trajectories starting with 1g for the whole trip and ending at 1g for a few minutes. The former is a full-up torch ship; the latter is a Falcon 9 Heavy. At one end the trajectory is pretty much a straight line and at the other it's a Hohmann orbit and all the others are in between.
So an in between torchship would have an in between trajectory -- straighter than a Hohmann orbit, but curvier than a 1-g-all-the-way orbit.