Update: This weekend I bolted up the front end and drained the oil from the front diff. There was almost no oil inside, and a few shards of metal came out. I refilled it and tried it, just to be sure, and the problem is still very much there. Probably a ring gear. So much for borrowing the neighbour's tractor to save myself some work. I'll see what he has to say. Thanks again everyone for your help on this.