Some basic ignition info ...
Normal wiring of coils is a +12V feed directly to the coil. The other side of the coil is wired to earth via the timed switching provided by the ignition system.
Think of a points-type ignition system. When the points are closed, the coil is powered up and there's current flowing. Points open, no current. If the engine is stopped at a position where the points happen to be closed and the ignition is switched on, current will flow through the coil and it will get hot. Quite hot.
Some electronic ignition systems will do the same thing. The default switching is coils powered up until signals start coming from the pickups to tell the system when to switch the coils off and on. The Dyna system on my Guzzi is like that. Leave the ignition on for a while and the coils start to cook. Stupid way to build an electronic ignition system in my opinion.
However, Ignitech systems are a bit smarter. Their default is to leave the coils un-energised until the engine is cranked, so the coils shouldn't heat up when the ignition is switched on with the engine not running.
So why are your coils cooking? it's highly unlikely that both the ignition boxes you've tried have the same fault, so we can assume a wiring problem. For some reason the switched (negative) side of the coil is getting a path to earth that's independent of the ignition system (as AndyW suggested). This could also explain your weak spark. You're not getting the full voltage drop at the coil when the ignition system interrupts the primary current.
Look for bad insulation or incorrect wiring between coils and ignition system.