Nick Rosenkranz is probably right that, as a matter of the strict formal “rules” peddled by some usage books, “Whomever you’re writing for will appreciate…” is correct, just like “Whomever you elect will serve….” Nonetheless, in my own writing, I’d use “whoever” in both of those cases: (1) virtually no one will recognize that it’s an “error”; (2) some of those who are familiar with the distinction will (like Garner) think “whoever” is actually correct; (3) if you use “whomever”, virtually no one will think it’s incorrect, but they’ll generally think it sounds highly stilted; and (4) using “whoever” will contribute to the salutary goal of hastening the death of the “who”/”whom” distinction. If a student of mine used “whomever” in that context, I’d suggest changing it to “whoever”.

Which means you should “whomever” if (1) you care about the strict formal “rules” and (2) you don’t mind (or positively embrace) that some people will think it’s stilted (or will think of you as someone who writes that way); or (3) if you happen to know that you’re writing for an audience that knows and cares about the difference.

Myself, I do generally respect “who”/”whom” — but virtually only in formal writing — and even then I might sometimes try to omit some “whom”s if I thought I could get away with it.