Success!!!
First I tried what Dangrouche said and nearly punched myself in the face
when my rag slipped. That sucker is on tight!
Then I broke out the industrial hair-dryer and heated the sucker up a little. Put a rachet extension through the hole in the end of the handle, stood on the ends of the ratchet extension, gave a light yank, and presto, the handle pulled off. It does look like they glued it on.
Now, it certainly appears they didn't make this very servicable. In order to get the rod out you must grind the weld off the pawl pin, remove it and the pawl, then pry the handle open enough to slide out the rod. WTF were they thinking?
I think I'm just going to cut off the old threaded part, weld on a new section, thread it and make a new button from some 1/2" rod stock.