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.
It might feel strange to include happy client testimonials in your out-of-office responder, but doing so is easier than you think. A quick note that suggests they read the testimonials if they’re interested in a product or service you offer is an easy inclusion or postscript to your email. Just limit the amount you share to one or two.

I read it as coming from a person who was overly frustrated with their regular OOO being ignored. It’s one of my pet peeves – the OOO clearly says I’m not there and to contact Bob, yet the sender continues to reply, never contacts Bob, then blows up at me when I return that their work is delayed. I would love to be able to send something like this message in the letter but it wouldn’t fly at my office.
iOS is offering a feature to set an autoreply for all incoming calls. Instead of merely rejecting the calls, you can send back pre-set messages while you reject it. You have an option to set three quick response message to send back while rejecting the incoming calls.