You could take the path through the systems with permamines with transports, you can clear the mines with cleanup drones.
And for the superfortress, I mostly attack them with my whole fleet at once, ignoring other stuff.
And yes, you can use lightning warheads, but you should make sure there aren't troops in the way of you target, or they might make them explode too soon.
Also you could post a save and let the people here try stuff, or ignore the system(s) till you can handle them.
Lastly, if reinforcements are realy bugging you, try taking out the command posts (not command station or that too if you're sure) on the planet (with a bunch of fighters or something).
Hope something helps