Did you try the following Recovery key combination as in your case <kbd>Shift</kbd>-<kbd>Option</kbd>-<kbd>command</kbd>-<kbd>R</kbd> mayb ehlep 

1. <kbd>Command</kbd> - <kbd>R</kbd>: Install the latest macOS that was installed on your Mac.

2. <kbd>Option</kbd> - <kbd>Command</kbd> - <kbd>R</kbd>: Upgrade to the latest macOS that is compatible with your Mac.

3. <kbd>Shift</kbd> - <kbd>Option</kbd> - <kbd>Command</kbd> - <kbd>R</kbd>: 
 Install the macOS that came with your Mac, or the closest version still available.

See if your High Serria is still available from it. I think it should be as you can still get it from App Store.