I think the problem is that “at your earliest convenience” is a formulaic convention that uses explicit, almost exaggerated politeness to basically issue a stern direction, meaning “as soon as you possibly can”. When you turn it into “at my earliest convenience” it’s unclear if you mean “whenever it’s convenient for me to get to it” (what the words say) or “as soon as I possibly can” (what the meaning of the formulaic original is). Or else it sounds like you didn’t quite understand how “at your earliest convenience” works.
As for this one I think it’s fine for internal particularly if someone can “read it in her voice” and knows she’s quirky but I’d probably just do a short one for external (or none? because I’ve heard there is some kind of security risk with them?)

[BUSINESS] is in no way endorsing or not endorsing said holiday, nor encouraging or discouraging employees of all demographic clusters to engage in celebrity activities. Thank you for your consideration during this festive or not-festive time.
I don’t think it’s rude to do the deletion, but it’s pretty rude to not give some sort of Plan B besides “Wait until I decide I am ready to deal with you.” I’m sure it feels lovely to set up if you’ve usually got a lot of annoying people clamoring for your time on matters that aren’t nearly as urgent as they think, but to not even offer a “in case this is urgent, contact X” fig leaf just shows you don’t care.