I can see the symptoms that you're having being caused by a problem with your main grounding back to the battery. There's no need for an "extra ground" to the starter solenoid. Electricity follows the path of least resistance; if there's a problem in the original main ground cables, a lot of current can flow through your "extra ground" and that can cause some weird problems.
Honestly, if it were me I would be looking real hard at your main ground cables, AND disconnect that extra ground wire to the starter relay bracket. If anything, connect that wire to the radiator support or inner fender away from the solenoid. Your best approach at this point, is to get the main power and ground wiring back to an original, good state. No fraying or corrosion on the cables or terminals, ends bolted tight to clean, bare metal.
Did you replace the battery ground cable with a new one? And did you ever try using jumper cables to substitute, or test ground, the engine to the battery?
I work nights; it'll be morning before I'm back on.
Good luck!