Seems VERY similar to my situation before I got it mostly fixed. My car had the exact same "MAF waves". Step on the pedal, MAF briefly gives a proper value, then falls, then comes back up a bit, falls, comes back up, falls. Each time the bounce gets lower and lower.
My car ran so poorly with the MAF plugged in, I drove with it unplugged just to be able to achieve high way speeds. The car was just plain gutless, and would slow to a stop up hills.
I would recommend a few easy, free tests:
First, unplug the MAF and see what changes.
Then unplug the vacuum line that goes down to the turbo vane actuator.
When I unplugged the vacuum line, it was like this weird...'calming of the storm'. Where my car had low power, but it...worked. I step on the pedal, it went faster. All my MAF graphs immediately whipped into shape, and it worked perfectly, just without the boost.
I eventually narrowed my issue down to my turbo vane actuator rod being out of adjustment and over boosting immediately, so my car would actually trip into limp mode at the very first throttle demand. It would literally go into limp mode on flat ground within .5 seconds of being started up.
When the computer trips limp mode, it cuts fuel heavily (among other things). So you've got low power on top of low power conditions.
When I disconnected the vacuum line (effectively removing the turbo from the equation), the turbo could no longer overboost and trip limp mode, so the computer spit proper fuel into the car based on proper MAF values.
But it could be other things too
