The easiest method I have found to remove the barrel pin is to set the front trunnion on a big chunk of steel and drive the pin out using a pin punch and big hammer. The more solid the backing the quicker it will come loose, so don't try it on your table (unless your table is made of concrete).
I have a chunk of steel that must weigh about 35 pound and is shaped like a big plus sign that I set on end on the floor in my garage.
Using that and my drill press my son and I managed to remove all the rivits and barrels from six Romys in one evening.
Using this method I have never ran into a pin that would't move after a couple good whacks, just have someone hold it as level as possible.
I even use the same chunk of steel, a big hammer and a big brass drift to remove the barrel from the trunnion.
They use some really tough metal for the trunnions and I have never messed one up.
Sounds quite Redneck.
I would get a press, but I have never found enough of a reason, except maybe to press bearings on a Ford 9" axleshaft. Anyway, I can get another parts kit for the price of a press.
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