To "me" or not to "me", that is the question

I'm in a bit of a quandary right now as to what kind of grammar to use around Amy when it comes to subject vs. object forms of pronouns.

The thing is, I was taught to use the subject form ("I, he, she") in certain constructions, but it seems to me that the object form ("me, him, her") is more natural to a large number of native English speakers.

The subject form is more correct according to conservative, prescriptive grammar; it also matches with what German (which inflects more strongly than English) does. But I wonder whether I should use this form or whether it's dated and unnatural.

The classic example is comparison statements. Does one say "He is bigger than me but she is exactly as big as me" or "He is bigger than I but she is exactly as big as I"? (There is, of course, also "He is bigger than I am but she is exactly as big as I am", where I think everyone uses the subject form of the pronouns, but that seems rather stilted to me, too, as the default form.)

Another example: Amy showed me a picture she had drawn in kindergarten and explained to me who the people on it were: "This is Anne and that am I and that is Nea". Fine in German ("das bin ich") but not only is the verb wrong for English (I think), the pronoun form is also questionable. I think it should be "...and that's ___" (with "is" rather than "are") but I'm not sure whether to say "and that's me" or "and that is I".

And a final, also classic example: responses such as "Who wants some cake? — Me!" or "Who spilt the orange juice? — Not me!", where conservative grammar would have "I" in each case (and German would have "ich").

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What do you think? "I" or "me" in that sort of sentence?

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And because I like polls: what is the most natural/spontaneous form you would use in the following constructions?

[Poll #1365332]

Jennifer's birthday

My sister Jennifer came up north for her birthday and had invited family for a celebration.

We had rented a car for that (to get the cake there etc.), so we drove up there this afternoon. (And I ended up driving back to fetch Stella's allergy emergency kit that she had forgotten.)

This time, not only the immediate family were there (that is, my parents and siblings with spouses and children), but also an aunt and uncle with their daughter and grandson and also two other cousins with their children. (Well, the older daughter of one cousin hadn't come.)

It was good to see my cousins again since I rarely see them, and to talk a little; apparently, they're both living in or near Hamburg now.

Various kinds of cake; and in the evening, some soup that Inka had made that was very delicious.

Better late than never: Pi Day

Happy Pi Day!

It's 3/14 in that curious middle-endian American date format!