Hello. It sounds like you might have an unmetered air leak on the vehicle. This situation could be cause by a bunch of things though and it might have to go to the dealer for diagnostics but I will help you as best as I can. It could also be fuel pressure related.

First the air leak. Remove the engine vanity cover and take a look at the back of the intake manifol. I believe on this vehicle you will have two hoses that are on the back of the intake. They often become "gummy" and develop leaks in the hose. You should be able to know by feel if they are gummy or if they have a whole in them. This is caused by the valve they are attached to failing(called the liquid vapor seperators). When this happens there is a small vacuum line under the intake manifold that goes also that you will not be able to see. If they are gummy they should be repalaced along with the pcv plate on the back of the intake manifold and the coressponding vacuum line. The intake manifold will need to be removed for this repair.

The next thing could be a bad fuel filter and pressure regulator. The only way to know for sure would be to replace them or have the dealer perform a fuel pressure test with and drive the car to see if the fuel pressure is dropping under load.

Lastly, you can check the dealer can check the multiplicative and addaptive values stored in the DME (digital motor electronics) module. If one is a negative number and the other is a positive number this indicates a bad mass air flow sensor and it should be replaced. I know you have said that you cleaned it but this does not alway fix it if it has failed.

I hope this is helpful. Let me know if I can help you further by answering more concerns.Thank you.