2000 Dodge Neon stopped while driving at low speed, able to restart immediately but stopped again

Travelling at low speed, less than 10mph, engine just stopped with no stuttering and all electrical still running. I was able to restart immediately but same thing happened within a few yards of driving. I left it parked for maybe 30 minutes. Whole episode repeated. I parked again and sat for another 20 minutes or so. Started up and was able to drive for a few minutes, shut the engine off while I filled up the gas, restarted and drove home with no problems.
Theories so far…faulty ignition switch, fuel pump (probably not this), overheated ignition module…my “mechanic” did some online research and came up with something about a wire near the exhaust that gets overheated and shorts then cuts off the engine.
Anyone had this similar issue? How did you resolve it?