This should not be the problem, but might as well disconnect the Brown “I” wire from the starter relay/solenoid.
Also disconnect any radio noise suppressors from the positive side of the coil.
Since you’re disconnecting the easy things, might as well disconnect the brake warning lamp circuit down at the brake H-block.
Neither of these should cause your problem, but it can’t hurt to rule them out and keep them out of the loop.
Since you now have a new key and tumbler, it should also be easy enough to remove the ignition switch from the dash. If you do that, then there is no way for it to ground out any of the circuits. At least not through the switch itself.
If it still has the problem, then I would think the fault is within the ignition switch itself.
I guess my first question should’ve been, are you still running the stock of Dura Spark ignition? Or something else?