A torch to heat them up and a BFH? But seriously,would a Drum puller work? Is there an access hole on the Backing plate to use a Brake S**** to "Loosen" the Star wheel adjuster?
Put the nut back on even with the end of the threads. Then beg barrow or other a hub puller that has 3 legs that attach to 3 lug studs. Tighten up good and tight ,smack puller screw head firmly with a BFH. When it comes loose you will see why I said replace the nut first. That style puller is also used on pre 48 Fords and some Mopars to the 60s.
That Ebay one maybe might do the job but the real deal ones have loose legs. And the best of those have a cross bar that fits on the puller screw that you can hit with the BFH to really tighten the screw. A lot of tool rental places have these.
Put the nut back on with the cotter key, leave it a couple threads loose, drive till you hear a pop, or two pops if you need them both off.