The car shouldn't fuel cut (it's actually spark cut guys) at stock boost levels unless it's running very rich. Do you have a boost gauge and what are you seeing?
My car did exactly what you are describing when my wastegate actuator went bad. Just pull the vacuum hose leading to the WGA off the block with the car off and blow into it. It should be like blowing into a wall, if you can blow through it, you need to replace the WGA. My stock one was replaced once under warranty, and I replaced that one shortly after my warranty ended with an ATP.
I also have caused my car to cut spark many times when tuning with the AEM FIC. Even after putting the AEM in bypass mode (stock), I was still able to hit cut because my fuel trims had gone off the chart due to my O2 manipulation. It occurs anytime the PCM drives 100% duty cycle on the injectors. A stock car rarely needs over 80%, but fuel trims can easily add 20%.
I don't think you need to go investing in a piggyback to solve this problem unless you want to go down that road for other reasons as well.
If the wastegate is good, I would find a friend with an OBDII reader and check your fuel trims. Autozone may be able to read them for you as well, but I think their scanner only reads codes, not parameters. If they are very high, as in the +20 range, it can be a couple of reasons, but most likely a bad O2 or exhaust leak. You can also reset the PCM and the problem will go away temporarily.
Try the WGA first and report back.