P5 It is impossible for all beings to fail to exist (entailed by P2-P4)

No, that's not entailed by P2-P4. It's still true of course, just entailed by the proposition you forgot to add: "P4.5: At least one being exists".

I don't know if you have a math background, but I have enough of one to have had drilled into me that a "for all" is useless if you don't also have an "there exists" somewhere in there.

From that P6 doesn't follow either, as P5 only requires at least one being to in fact exist, but doesn't say anything about this being's existence being necessary.

P7 is just making stuff up isn't it? Like, you haven't proven that your being that it was necessary for it to exist was unique. Nor have you proven that if isn't unique, that all beings that necessarily exist have the same level of greatness. Without proving either of those things I can just posit "take a being that necessarily exists. Now suppose another being that necessarily exists, but is twice as great as that first one". There you are.

And I'm not sure how you get to C. Like, you started with the contradictory premise P1, so presumably this is a proof by the absurd where you're supposed to unveil a contradiction that disproves the first premise. Where's the contradiction here, does it only show up at C?