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.
There ought to be a word - and perhaps there is, in German - for the mix of feelings that accompanies composing and activating a holiday out-of-office message. There's smugness, of course, and a gratifying sense of laying down one's virtual tools after a horribly long shift. But for many of us, these nice feelings are tempered by the knowledge that in two weeks, refreshed but depressed, we will have to trawl through hundreds of emails, many of which will be conference room notifications for meetings about crises that have passed.

Tip: If you’re not sure how to leave a good voicemail, check out the most effective voicemail script ever and how to end a voicemail that keeps the sales conversation open.
The marketing tactics of businesses should be focused on customizing the client experience to make each interaction meaningful and valuable. Personalizing your automated replies makes your customers feel good (if you do it right) because it helps you say something that’s actually helpful and targeted.