Over-sensitive keys on A1278 replacement keyboard.

I had recently purchased an A1278 replacement keyboard from iFixit to fix a space bar that had gone bad due to water damage, but was having an issue with one of the keys not working, which gradually spread to more keys, and then the whole keboard stopped working altogether. I ordered another replacement, and now I'm having different issues:

This time, the issue seems to be that several of the keys are overly sensitive. For example, the S, space bar, and arrow keys will often trigger unintended keystrokes even if I'm not pressing on them, or if I'm only lightly resting a finger on them without pressing down. I found that if I remove the keycaps, the unintentional keystrokes stop, and I am still able to press the key domes directly to use the keys. This isn't ideal, so I'm trying to figure out a way around it. I was able to remove some of the arrow keycaps from my old keyboard to get rid of the sensitivity/spontaneous keystrokes. It seems like the newer keycaps may not be the proper fit or weight for the new keyboard and are triggering unintentional keystrokes. This doesn't work for all of the keys, though - the S key still triggers keystrokes even if I'm just resting a finger on it. Swapping the space bar had an even worse effect - the old keyboard's space bar caused the new keyboard to trigger the space key continuously.

Any ideas as to how this might be fixed, or if this might be a defective keyboard?