I tried my usual method of making a small bubble of solder that extends across the width of the component to cover both sides, and then lifting the capacitor away once it had separated. However, I found the CPU to be a much too strong of a natural heatsink for this kind of casual work. Part of the issue was that the processor itself was a highly concentrated thermal mass, but also the ROHS solder binding the component to the PCB, which has a much higher melting point than traditional leaded solder. I switched to hot tweezers and the capacitors lifted away easily.
All three of the capacitors were the same physical size. Two of them measured 1uF, and the third closer to 0.5uF. I believe the last one was actually in error, as it was physically damaged, so I opted to use 1uF as a replacement for all three.
I then used a fine-pitched solder paste and hot air to attach the new capacitors. It was a struggle, again, due to the high thermal mass, but the solder eventually took and the components attached.
I plugged it into my motherboard and the system booted up perfectly. I've since put it through its paces with Prime95 and it appears to be stable. This is an expensive processor, so I'm glad that I was able to salvage it with this repair.
The attachment 20221217_005111_resize.jpg is no longer available
The attachment 20221217_005232_resize.jpg is no longer available
The attachment 20221217_005607_resize.jpg is no longer available
The attachment 20221217_010010.jpg is no longer available