Everpix’s servers are probably going to hate this, but users will love it. Picturelife (my favorite of the Everpix alternatives I tested, has made an Everpix-to-Picturelife importer. If you received a link to your Everpix archive, you can just plug it in to the importer and walk away.
Best of all, the entire archive won’t count towards your storage quota. And the Picturelife team managed to put this all together in less than 24 hours.