Well, what do you know! I updated from Wordpress 4.01 to 4.1 (I was delaying this operation until the translations issue was solved, but in the end I decided to update, just in case).
And after the WP update was completed, it prompted me to update the Automattic themes translations, TwentyFifteen & co. And when this update was done, MY translations appeared in the Polylang settings panel as they should have been from the very beginning.
Then, just in order to make sure that the WP update completely solved the problem, I rerun the database restore script. This time the restore went without any issue, the translation strings are there and the local site is finally all right.
Conclusion: the DB restore under WP 4.01 caused the translation to be lost; upgrading to WP 4.1 solved the problem.
A big thank you to the plugin author for the quality of the support he provided to us!
