4. A miner has control of 51% or more
All 4 of these create a P inconsistency, and so the LCR (longest chain rule) kicks into action to resolve them.
Seems that is a Consistency (as you said the LCR can rewrite all the blocks under 51% control) and Access violation (and the 51% attacker can't censor the block solutions from the 49% and censor any transactions), not just a failure of Partition tolerance. But it can also be interpreted as a failure due to not being able to tolerate a 49% partition and thus the longest chain rule kicks in.
I am still reading the remainder of your post.
However note that in the following linked thread:
I pointed out that the 51% rule is fundamental to any consensus system, thus you will not avoid this in your design either:
We technologists have looked deeply for an alternative to Bitcoin, that would eliminate its 51% attack vulnerability, and have concluded with the
51% Rule of Decentralized Agreement, which implies that no decentralized digital currency will ever be able to (sustain an) escape from the desires of the majority of society.