Connecting the heater
This one is in my neck of the woods as I am an electrical engineer specializing in electrodynamics.
Use the magnets to press the electrical contacts together. That is a great idea.
I would further recommend supporting the entire rocket by them in lieu of the rod (see above :)
Making it work:
What are the electrical tails on the magnets for? Are they to reverse-saturate the magnets? This would effectively 'turn the magnet off.'
If that does not work then try:
Couple the magnets via iron cores that remain on the launcher. Wrap the cores with coil-wire. When it comes time for separation use a large pulse of electrical flow to induce a magnetic field of opposite polarity of the permanent magnets this will literally push the rocket away from the launcher. Make sure the coils are in series to ensure a synchronized release.