I think using his or her would be OK with the grammar pedants, because at least these words are in harmony with the singular pronoun Everyone. I can say this with confidence because I am something of a grammar pedant. I furrow my brow and wag my finger at Michael Swan, who is poisoning people's minds with the awful notion that the plural their can be used with Everyone. Yutori kyoiku at its worst! It needs to be resisted and pushed back at every occasion.
This situation reminds me of "ら抜き言葉"; that is to say it is a spoken convention that breaks the rules of grammar in a way that is generally forgiven. If I were a teacher of Japanese, and a student asked me if it's all right to drop ら, I'd be reluctant to say "yes", even though many Japanese nowadays drop ら from conversation. Likewise, if I were teaching a group of students English, I would tell them that Everyone is always singular, and that they should not use plural verbs or nouns with singular pronouns. Call me a perfectionist, but I think you need to set a high standard when teaching this stuff, so that you have a better sense of when (or if) its OK to bend or break the rules.
To be sure, nobody would think twice about your examples B and D - they both sound correct-ish. They are both used in everyday English. But, just as with ら抜き言葉, they are both incorrect. Professor Swan may use the euphemism "less formal", but they are indeed wrong. Here I think we should strive for a bit of perfection.
So, Hirashin-san, your question is a trick question: I think all of your sentences are broken. Your question then becomes one of preference. A, B, C, and D are all equally fine if you ignore the error, and they all adequately convey what you intend them to convey. But I invite you to look upon Michael Swan's advice with a bit of suspicion