Hi, Luke, and welcome to 2CarPros.
You are asking me a loaded question. Lol Is the vehicle overheating not that you installed a thermostat? Also, you really shouldn't run without one. It takes the engine longer to warm up, and it can actually cause it to overheat because there is too much flow to allow coolant to cool off in the radiator.
As far as the cat thing (by the way, I loved that description and needed a good laugh) Can you explain what exactly is happening and where the noise is coming from? As far as the push button start, you should have to have the key in the run position and not ACC for it to run, so I'm not sure what happened with that.
My recommendation is this. Since I'm not there to actually see what was done to it, drive it as much as you can near home and see if anything acts up. If it seems dependable, I would try using it. In all honesty, 200 miles one way really isn't too far, but I would hate to say go for it and then it fail for you. Try what I said. Drive it as much as you can near home and see how it does for you.
Let me know if you have other questions or need anything.
Tuesday, June 4th, 2019 AT 8:25 PM