Creating a language file would be the best option. I doubt you're doing changes directly in the POT file. Instead you will need to create language files. Kindly follow the link
premium.wpmudev.org/blog/how-to-translate-a-wordpress-plugin/ to translate the plugin to your language.
And, the translated file names should be,
another-events-calendar-{YOUR_LANG_TAG}.mo
another-events-calendar-{YOUR_LANG_TAG}.po
Also, I would suggest to place your language files under /wp-content/languages/plugins/ to keep them working ever.