That was "matter", now this is Alex!
I don't think you need the CELTA as well.
Most jobs ask for "CELTA or equivalent", so your job on your CV and cover email/ letter is to prove right at the top that your qualification is more than equivalent. The most important thing is the number of hours of observed and graded teaching practice, and the second is that it was at a well respected university. Then you could mention any other similarities to the CELTA such as teaching methodologies covered, textbooks you used with the teaching practice groups, materials used in your own teaching training sessions, etc. If you had any professors who have published anything well known in the profession, that's also worth a mention. And I'd also explain what jobs in the US that cert would qualify you for, i.e. who does accept it.