We had one.  The first ones had a 4 cy Continental engine.  Not enough power.  A couple of years later Massey put a 6 cy in it.  Power then was O K, but you are correct, it did not like mud.  We put push boards on the front of a Farmall C to push on the wagon to help it.  I used to stay home from school push it.
The front end was the same set up a the New Idea pickers.  Unsure if the parts would interchange, the gathering chains for sure. The later ones had a rubber shucking bed in them, and did a cleaner job.  Also the later one had a fan above the bed to help keep the fodder on the bed.