Static front page – going against the grain

If you’ve got a front-page.php template, I think this will get used, even if you change the Reading -> Static Page settings:

If you read https://codex.wordpress.org/Creating_a_Static_Front_Page you’ll see:

‘On the site front page, WordPress will always use the front-page.php template file, if it exists. If front-page.php does not exist, WordPress will determine which template file to use, depending on the user configuration of ‘Settings > Reading ->Front page displays’, as follows:’

You could rename your new home page template to be front-page.php and rename the old (current) front-page.php so that it can be used as a template on another page.

Another useful read is the template hierarcy:
https://developer.wordpress.org/themes/basics/template-hierarchy/