throw flux on the joint to desolder and soak the solder braid in flux and use the yellow nasty sticky flux rather then the clear low residue one. You need stronger shit for old non leaded joints. Also you can put solder on your braid then press the braid against the joint then the solder iron against the braid to start the wicking process.
Doing this may help. You can put a big glob of solder down. Your tip should not oxidize that fast though.
I recommend you melt a big glob of solder on top, melt the whole joint, and use a solder sucker though. If its being a bitch you can melt it and use a duster-spray/compressed air in a tiny nozzel like the straw to blow the solder inwards, but you get little spikes of solder that go all over the place. With really big caps you can yank on them a bit with no consequence they seem to be built pretty tough, I have seen them shot out of black powder guns before lol. You can like melt one joint, pull on it a tiny bit to move it up, then do it on the other joint, and kinda walk it out. When its almost walked out you add more solder to actually fill the joint so you have thermal transfer and you keep walking it. In the end you might get a tiny little connection that you can just rip off,
basically the strength of electrical solder tensile is roughly 6000 pounds per square inch.
So if you have
6000=640mm2
x=0.1mm
so a little 0.1mm bond has a tensile strength of less then 1 pound. I would not worry too much about ripping it a bit when its almost done and you have some pissant contact between the capacitor and a VIA for instance (fucking super annoying).