Car started overheating out of the blue?

I'm thinking so. The shop didn't state that they did any testing to make sure before diving right in. 1st I was told the water pump. So, I Okay'd the replacement as well ask them to go ahead and replace timing chain since it's right there. After they did this, they test drove it. It still kept overheating. So, then the shop tells me that the header gasket must have been damaged at the same time as the pump and that to replace that it was going to be over 2,000$ because they would have to tear the motor apart again. Now I'm stubborn and decided that I've obviously made my bed with this car so I mise well lay in it. I asked if it would be better just to replace the motor. (Now I had just bought this car and only had gotten to drive it 2 weeks before all this happened which is why I'm being so stubborn because I was determined to not let bad juju beat me) The shop states it would be roughly about the same cost lol. Again, there was no mention of them doing any test to verify if said parts indeed were bad. I wait from August to November for them to locate a motor. (Basically, they parked my car and forgot it. ) So, I have them order motor. Take November and December before they get to the car. Finally last week I'm told the car is done, no leaks or overheats. I go get it. I drove it maybe 1/2 a mile to a store, parked and I let it sit and idol for a min. After idling for almost 10 minutes the car once again overheats. I happened to notice that the overflow cap for radiator was off. Maybe blew off from pressure or wasn't threaded on. I take car back. Tell them what happened and how I'm so very not happy. 5,000$ and the problem is still not fixed, even after putting a different motor in!

Just received a call from the shop. They believe it's the overflow and cap are stripped threads and isn't staying on. Now this is the original overflow and cap. Did I seriously just shall out a butt load money and had 7 months of my time wasted and replaced a bunch of parts that didn't need to be replaced? Is it possible it was the overflow and cap all along? What do I do?