The functionality that you are asking is not available exactly as you want. We understand the usefulness and will consider in future.
You may still create a status page and modify the iframe code to show only the required part. You need to tweak iframe style properties (width, height, margin-left and margin-top) accordingly.
You can also check with our custom dashboard public option. You can create a dashboard with one current status widget with the specific monitor you need (screenshot attached) and use "Share This" > "Make Public" option to get a public URL and embed it in your site.
If the design is still not matching with your requirement, you can make an API call to get the status of the monitor with the public dashboard key.
You can get the widget id and dashboard public key using browser developer tools.