About the only part you can't get is the rubber base. If the element is still working properly then it is a reasonable machine to consider rebuilding.
Skip the long breaker bar....unless you are talking about a 2 footer or so. Avoid the hammer and screwdriver technique unless you can get a really nice direct alignment,,,,the angle you have to use with the base attached does endanger penetration of the brass.
If the paint is gone on the base I would recommend HEAT....play a propane torch around the rim of the elemenbt...with propane this takes some time....around and around slowly and patiently. Once you get it hot, I mean real hot and the propane does not have enough heat to melt the brass but not so hot as to melt the solder at the element terminals, set is aside....no cold shocks or anything, just let it cool naturally to the point of being able to handle it without burns.
Now, using the filter wrench tool, which by the by is called a La Pavoni boiler element removal tool, at least it mentally helps that you think of it in this formal manner, Enlist the help of a willing associate and one person holds the machine base upside down between the knees while gripping the boiler with two hands while the other person operates the wrench. Concentrate all of your thoughts on that wrench boiler connection. Now try to TIGHTEN the element CW even if the slightest bit. this will break it free and try to loosen CCW. If you have gained even a millimeter you can now add a drop of oil on the first thread that wiggle back and forth back and forth until this movement gets a little bigger and bigger and you have worked the oil in the thread. This entire maneuver of course requires a total concentration of your entire bodily force into your arms hands shoulders upper body pectorals and the entire abdomen so don't try it on a revolving stool. The human generated force to remove the boiler element from a 1977 La Pavoni is likely off the scale in Joules but it it well into the causing one to break wind range.