The filename of the template chosen for pages is saved in a post meta field called _wp_page_template, which you can get e.g. like this:
$template_filename = get_post_meta( get_the_ID(), '_wp_page_template', true );
Now you have a file name like example-template.php, with it you can determine which template to load, if you named it right, so you could e.g. do:
$template_fn_wo_ext = substr( $template_filename, 0, -4 );
Which does remove the last four characters, so you get example-template, now you could do:
$template_fn_parts = explode( '-', $template_fn_wo_ext );
Which gives you back an array with the string parts, splited at the -, e.g. $template_fn_wo_ext[0] contains example. So you could use this to load your template like this:
get_template_part( $template_fn_wo_ext[0], $template_fn_wo_ext[1] );
This should get you an idea and started, but it is just exemplary, so do the fine tuning and fitting it to your needs is likely needed.