In my line of work, I have worked closely with HR and have been involved behind the scenes in things like this. I have seen PIPs that are fair and actually used as intended, and I have seen PIPs that are so demanding, it’s beyond obvious that they want you to fail so they have an excuse to let you go. Which do you think this one is?
I’m getting the vibe that this is the latter. I am not at all familiar with working under a union contract, but in a hostile situation, I would consider the likelihood of success of going to HR and saying “let’s skip the PIP that you can’t enforce anyway, offer me a reasonable severance, and I’m out of your hair today/this week.”
You don’t need to be running yourself ragged pretending to try to meet their unreasonable demands at the same time as you’re job hunting.