Since you've already replaced the starter, ignition switch, and TIPM, here are a few more things you might want to check:
Wiring and Ground Connections: Inspect the wiring harness and ground connections associated with the ignition system and TIPM. A bad ground could cause unexpected behavior.
ECM (Engine Control Module): There could be a fault within the ECM that is causing it not to recognize that the key is removed. If the ECM is stuck in a "run" state, that might explain why the engine continues to run.
Neutral Safety Switch: Check the neutral safety switch (if applicable) to ensure it's functioning properly. A faulty switch could send erroneous signals.
Relay Issues: There might be a relay issue in the TIPM that’s preventing the engine from shutting off. Sometimes, relays can get stuck in the closed position, which keeps the engine running.
Faulty Sensors: Investigate the crankshaft position sensor or other related sensors to see if they're sending incorrect signals to the ECU.
Last Resort - Wiring Diagrams: As a last resort, you might need to pull out the wiring diagrams for your model and trace the circuits linked to the ignition system to investigate any anomalies.
Try to work through these suggestions, and hopefully, one of them will lead you to a solution. Good luck!