One way to accomplish this is with Microsoft OneDrive. The main barriers to this method are:

  • You need a paid Office365 account to get the 1 TB storage
  • You need to be on Mac OS 10.12 or newer

It has the same functionality as Google Photos where you can have all your photos automatically upload from you phone. Then you can sync them to your computer using OneDrive for Mac.

Sounds like you weren't planning to upgrade Mac OS, but if you already have an Office365 subscription and the upgrade would make the difference, this could be an option.