The accent you’re embarrassed about took two whole countries to build.

That sound is a history rather than a mistake. It holds a first language, a second one picked up somewhere else, two sets of streets and whoever raised you, and no single place could have produced it. People with one unmixed accent are carrying a shorter story in their mouth.

Stop flattening it on the phone or in presentations, which takes effort and buys nothing. If somebody asks where you are from, give the whole answer instead of the convenient one, since the long version is more interesting anyway. Listen for where it thickens, and let it.