In my opinion, monitoring every phrase your page ranks for isn't a sustainable goal - there are too many variations and long-tail phrases being searched for. In terms of rank tracking, I tend to focus on the one or two higher-traffic terms I'm really targeting for a page, trusting that that ranking will translate into a halo effect of longer-tail terms and topical authority.
Rather than focusing on finding all of the phrases driving traffic to your page, try focusing on how much organic traffic each landing page is getting, and whether or not that traffic is doing what you want people to do when they reach that page. This will help you discover if the page matches the intent of the terms people are searching for. You should also take a look at the query data in analytics/search console to see if there are topics that your home page is appearing on page 2 or 3 for that you could create a more specific piece of content around - it's a sign that Google already understands your site is related to a topic, and just doesn't have a good page to send people to.