Upon bumping the starter with the key in the ignition, the entire car goes dead instantly. Like everything, no interior lights, headlights, dash door-ajar lights - nothing. It'll stay dead until I disconnect the battery, let it sit for a bit, and then reconnect it. Then it'll start right up.
If I don't wait long enough while disconnected, nothing happens when I reconnect the battery terminal. After the appropriate amount of time, everything comes back to life when reconnecting.
This is odd for sure. Did I miss how long ago you replaced the starter? I don't think it should be acting like a main fuse short to ground, but something in that circuit is not working properly obviously. Clean the ground wires and inspect all the other connections at the starter. Sounds like a fun one to track.