I know I said I'd update this with info for the other style of PCB, but it looks like I never got around to it, whoops. Better late than never.
If your K1000 has the type of PCB where the solder posts are further apart and cannot both be heated at the same time by the iron, it can still be relatively easy to remove, and this method works on both types of PCBs. The solution is simply to use desoldering braid on each joint, being extra careful not to heat it for too long or let part of the very hot desoldering braid touch the driver and melt it. I'm going to repeat that because it is very important: do not heat the posts for more than a few seconds at a time, and always be mindful of where the desoldering braid is because it will go through the driver like a hot knife through butter.
Chances are even after multiple passes with the desoldering braid, it will still be stuck with solder in one or two spots. If it's just tiny spots, or you can't even see any but it doesn't come out freely, you can try gently rocking the PCB to cause those little bits of solder to flex and eventually break. The keyword here is "gently"; trying to force it can quickly turn a money-saving DIY project into a very expensive repair.
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Also, if anybody wants more detail about any aspect of this, or has questions about other aspects of working on the K1000, feel free to ask them here or contact me by email.