Starts but will not run once put in drive cuts off?

Hello, does the vehicle stall out right when it's shifted into Drive or Reverse (any gear really)? Does it happen if you shift directly into Neutral?

And there are no diagnostic trouble codes setting in any modules, no check engine light on when idling in Park, and in this situation I would expect there to be, the shop should have told you if any codes were present when scanning the vehicle. You should be able to put the original ECM in the vehicle without having to program it. It will require an Idle relearn procedure, from being disconnected from the battery.
It might be a problem with the torque converter remaining locked up when it shouldn't be. The torque converter clutch locks up when under a cruise condition such as on the highway. The converter clutch should release when deaccelerating (coming to a stop or slowing down). It could cause a stall out when going from Park to Drive, I'm sure it might cause a thud as well.
Unless this is more of a stall out when going to take off in drive, and not an immediate stall out. Since putting the vehicle into Drive puts more of a load on the engine than when in Park, it could be a number of things causing a stall when trying to take off from the stop.
And are you able to restart it right away in Park again?

Okay, there was a campaign for a manufacturers defect in the transmission and/or torque converter, there are also quite a few technical service bulletins for the transmissions in these vehicles. As for the injectors being replaced, or a fueling issue, the shop should have been able to diagnose that pretty easily. With monitoring the live engine data with a scan tool, it should show if the engine is going lean (lack of fuel) when put into drive if that was the case. Or if the fuel injectors were losing a control signal from the ECM. You may want to try a better shop if they cannot give you more information. They should also have done an idle relearn after putting the ECM back in the vehicle.

There should be no need to reprogram an ECM if unplugged, we unplug them for testing circuits in many cases. It sounds like the shops in your area don't know what to look for. Are they not doing a full system scan to see if there are any codes stored?
And is the Check engine light on when its running in Park?

When you say a missing sound, do you mean a hissing type of sound? Does the engine have a rough idle to in Park? Can you keep it running if you were to keep your foot on the gas pedal a little as well as the brake pedal when trying to put it into Drive?
I'm asking because if the engine is not getting enough air to keep it running when put into drive it could possibly stall, so giving it some gas will open up the throttle plates a little and allow more air into the engine. Putting it into Drive does put a load on the engine.
Can you take a video with your phone of it running in Park, and then one with you putting it into Drive, so we can get a better idea of what you are experiencing.
The mechanic should be able to see something out of place with a scan tool, and be able to scan for codes, I'm not sure why they are not giving you more information.

You should be able to post a video right here. So when the problem first started you could keep it running by keeping the throttle plates open somewhat (keeping your foot on the gas pedal), but now you cannot? Or you can still drive it that way? Just want to make sure I have a clear understanding of the whole picture here. And its making a thumping sound when just idling in Park?
If you can get a video with the hood open and it just idling in Park as well, that might help. If you can keep it running with your foot on the gas pedal in Drive, thats makes a big difference versus it not being able to run at all in Drive. You dont necessarily have to go by the mechanics shop yet, we just need to get a better idea with more detail about its running condition. Its can be difficult to understand by just describing what you're experiencing. Im not sure why they would replace all the fuel injectors, without knowing what the issue is, really you shouldnt have had to pay for that since they did not fix the problem. I cant charge my customers for replacing parts if I dont actually fix the original issue.

Okay, and the oil is up where it should be also? Engine noises like that are not a good sign unfortunately. It sounds like the engine can't handle the load once put into Drive. Did you notice anything with the steering being difficult or anything else not necessarily having to do with the engine mechanically? I'm just wondering why the shops couldn't see what the engine was losing that's causing the stall, such as fuel pressure or air flow. Scan tool data can give a lot of information as to how the engine is running, and if the engine computer is compensating for any issues. Engine clunking or knocking noises that are very metallic sounding are usually mechanical type failures. But we need to hear it from the hood open and from inside the car if possible. Most issues will set a code when it comes to sensors or anything emissions related. Thats what the entire computer system and check engine light were originally designed for.