If I understand you correctly, your solution should work fine. The problem is your ground wire carrying the current for all of the lights in your assembly. It's a common ground for all of the lights. Pull it out of the connector (or cut it) and reroute to prevent further melting and potential damage.
It's just my weekend car. I ride in on an Ent during the week.
I picture this wandering the office halls.
I'm retard strong.