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.
Indeed, but my focus was on P alone (and also not to confuse other readers).
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.
I'm not disputing the 51% rule, no system can eliminate it, ever! However the consequences of it occurring in Bitcoin and other cryptos is truly disastrous due to the reasons I posted.
The best case scenario any system can hope for is that the actor with 51% majority can influence future events only, not the past! Because at least then, in the event of a complete system failure, you still have a true historical record of fact which can be trusted up to the point of failure.