It can be tricky to get them back into it - or train them to do it.
With my old horse he could do that well, and counter canter, so he wouldn't just change for the sake of it, you had to ask him. I did figure eights and then at the centre I would change the flexion a little, and slide my new outside leg back a little and sort of twist and then he would change.
If that doesn't work wait until you hit the corner on the rein, ask for the other lead with your leg and flexion, and if he doesn't change bring him back to a trot and the moment you feel him break into trot give your canter aid. Doing that a few times and he should get the drift.
I would do the figure 8, but with a slight twist. Without twisting, overbending or anything extravagant, come back to a walk for just one stride at X and then ask for the other lead. If you need to take few steps to adjust you flexion to the other side, by all means do it. The idea of coming back to the walk is to duplicate an extreme half halt. Coming down to a walk shifts the horse's weight onto his hind end if done properly, so his balance will already be in the right place to take the next canter lead. Once you've got it down to changing leads with just one walk stride, apply a strong half halt in place of it and ask for the other lead as if you were coming out of the walk stride. As you and your horse get more proficient at it, you'll be able to do the flying change with just a basic half halt. Good luck.
I would do a version of the figure 8. Go across the diagonal as part of your eight, then go around the ring once and then go across the other diagonal. Make sense? Also, I would do a few simple changes, then add a pole in and do the change over the pole(I would set the pole closer to the end of the ring than the X). After you do this for a bit, try to take the pole away and do the changes. Change the bend to the new direction, slide the outside leg back a bit and push the haunch in. Good luck!