You emphasise all the customer service style jobs you've had; or you say that you want to get customer service experience with a world leader company that takes service seriously.
This does not work in the current market for the kind of role we're discussing. The hiring manager is looking for criteria to turn the big pile of CVs into a small pile of interviews.
Being overqualified, or unexplained gaps fit the bill perfectly. It really does not matter how well tailored the experience, or how impressive the covering letter.
If you are applying to a company that has a "hiring manager" and are not a perfect match, you are making the first mistake.
The manager at Starbucks is not a "hiring manager". He doesn't care what's on your resume. He cares about three things: 1) Can I work with this guy? 2) Is he reliable/competent? 3) Is he going to steal from me/screw the other staff/piss off the customers/otherwise make my job more difficult?
Being overqualified, or unexplained gaps fit the bill perfectly. It really does not matter how well tailored the experience, or how impressive the covering letter.