The issue I have with these large ground planes isn't so much removing the leads; those can just be heated up and pulled out. It's the solder that gets stuck in the hole. No amount of heat, suction, or even heated vacuum pumps will work for some holes, and overworking it often ends up damaging or lifting the pad.
The best solution I found that was the easiest on the board is to apply new solder (which also has fresh flux) as a blob, then heat up the blob and let the thermal mass allow the leg to come out gently, without pressing hard into the PCB or the pad. Leave the blob on there and use it as a means to heat up both the pad and the via as you feed in a fresh leg through the hole.
The large thermal mass provides a good thermal connection to the via, and allows the insertion of the new leg. The only caveat is that you will have to rock the component in from one leg to another, if you only have an iron. It might work better with hot tweezers, but a proper set is expensive, and my tweezers are junk. It works fine with an iron though. Just pre-clip the leads to about half their normal height so that it will be easier to get in.
The hardest parts I have to remove are the large through-hole packages. There's no other way to get them off other than levering them, even if you use a pump, hot air, or whatever. I always worry about the pressure I'm putting on the board when I do that, and the fragility of the pads. It's also possible to clip all of the legs off and then they come out easy, but this is not useful when you are debugging the board or adding sockets to known-good chips.