If the orbit passes through the point opposite the departure direction, the same burn is required when the S/C hits the tangent circle to escape with the requisite excess velocity . Whether the S/C is heading north or south shouldn't make a difference.
Do others concur?
I do not. It does make a difference whether you are heading north or south as you want your velocity vector to be approximately pointing in the same direction as the Earth's rotation around the Sun at TMI.
On launch day on 8 November, PG was heading over South America at night in a north-east direction. If the 6 degree per day recession is correct, then in 30 days time (on 8 December) PG will again be heading north-east, but on the day side of the Earth. This means the velocity vector is pointing backwards, which is no good, unless you want to go to Venus. On the dark side of Earth, PG will be heading south east which is the right direction.
However, the angle of PG to the ecliptic plane will have changed. On November 8, the angle between PG and the ecliptic plane is the inclination of PG to Earth (51.6º) minus the inclination of the Earth (23.4º), that is 51.6-23.4 = 28.2º. On 8 December the inclination of PG to the ecliptic is the inclination of PG to Earth (51.6º) plus the inclination of the Earth (23.4º), that is 51.6+23.4 = 79.8º. The higher this angle the more delta-V is required to reach Mars. The higher inclination of PG on 8 December, plus being very near the end of the window may mean that PG may not have enough propellant to reach and then orbit Mars.
If the Russians can get in contact and control of PG before it re-enters and if its too late to send PG to Mars, a possible rescue plan could have PG fire its engine to put it into say a 350 by 600 km orbit. There PG will stay for two years until the next window arrives around November 2013. The period of the orbit being designed so that PG is in the right position for TMI in two years time. This will rely on the on-board batteries being able to sustain two years worth of charging and discharging, which they probably were not designed to do. Going for a higher apogee will mean less charging cycles, but PG will be passing through the Van Allen radiation belts. Using the Moon and the Lagrange points it might be possible to have PG hang around the Earth-Moon system and then dive to 300 km perigee for the kick to Mars in two years time.
So I think its possible that PG can be saved, but before this can happen contact needs to be made, which unfortunately has not happened yet.