I had loads of moss on one of my fields when I bought the land , it also had a thatch of dead grass on it . To get rid of it all I just went over with a hay bob set very low, so it was rubbing hard on the ground. That cleared all of the thatch and the moss too. I then overseeded with a patching mix of grass seed , it did the trick fine.
Panning of the land due to ploughing would really only happen if the field was ploughed on a regular basis to the same depth , so if it has been ploughed regularly in the past this could be one reason for it? However, clay forming a natural barrier seems to be more likely the reason to your problems. The clay is making a waterlogged bog of the topsoil . You can find out if this is the case by digging a few holes here and there. You would have to do them where animals (or people) can't run along and fall or trip into them . Just dig a hole say 24" square and deep enough to see where the topsoil stops without breaking the clay just beneath it .Water should then sit in the hole or maybe even fill it, if left for 24 hours . Then just dig the hole a bit deeper , leave again for a day to see if it drains away . Keep doing this till the water drains away , you have then found the depth that you would need to get to , to drain the field . It sounds like a lot of work , but it doesn't take long to dig the holes and you can do them as and when you want . Myself , I would just try growing alfalfa on it for a year or two . The roots would go really deep and allow drainage plus adding nitrogen . Then just plough it in and grow whatever mix of grass you want . If you don't need the field for grass you could always grow willow in it !!! that would soon sort the problem out .
cheers
Russ