Here is a thread from the past posted by forumnaut and collector Brian Rollanson. It has several pictures of his apart.
http://www.swordforum.com/forums/showthread.php?89616
While the thread is quite flatter and a bit shorter, the thread pitch seems spot on to that one. I would not necessarily dismiss it on the point of the threads as by the time of the 19th century spontoons, thread machining pretty well said and done (look t 19th century English fiirearms for instance).
Here are a couple of crappy pictures of my Hanwei reproduction that has a much finer screw thread along with a point to help guide the errant assembler. Brian's could have flattened a great deal just in use vs the one listed above that might be brand spanking new but still a couple of centuries old. We have all seen as new arms that are that old.
I am not familiar with other more recent reproductions of these but another trait to my own Hanwei (now discontinued but still on the shelves here and there) is that the langets are of mild stainless steel welded to the socket itself. That stymied me in going to age my own for my own purposes. I also added a fourth hole. I don't have great pictures of other period examples of the British model but they were manufactured abroad as well as in England. They supposedly saw service for half a century and were both hafted as "quarter" pike and half pike in length. The longer ones nine feet tall.
I'd love to see the haft fasteners of the one listed here and other examples. I ended up not fastening mine flush but used rose head nails but I see most originals now as flush rivets.
Was there any shoe on the haft? I wouldn't either necessarily say an orifginal was not rehafted. I think a lot of polearm collectors wonder the same things though and reproductions do go back in time.
Cheers
GC