This is a really strange one, and one I have recently experienced on my 2007 1.9 jtdm. Precisely the same fault. A new EGR valve was fitted and as soon as this was dome I got the 'MAF Sensor problems' which had not been there pre-EGR change. I tried cleaning - no change. I drove it 'un-plugged' - perfect. Cleaned again - no change. Finally convinced my third party warranty company that I needed a new MAF sensor. They would not pay for an OEM so my garage got hold of a generic Bosch, which is same part number and looks exactly the same, without the AR stamp. The cost of the part was about £100 and after fitting car drove much better, but not perfect, I would say about 90%.
But then it deteriorated, and after several hundred miles it was back to where it started. I convinced myself that the problem was the non OEM sensor and started hunting around for a genuine one. The cost seemed to be £200 plus. But then, all of a sudden, the car started to drive normally, and it has done now for a couple of thousand miles. Its back to how it should be, no hesitation, stuttering, rasping noises, but just delightful smooth driving. Why? I haven't got a scooby-do!
So why am I saying all this. The non-OEM seemed to have worked for me, but not initially, it seemed to take a few hundred miles to settle down. Good luck.
Don't listen to what I say, listen to what I mean ..............