I believe I found the best solution for this that doesn’t require a plugin.
Once your sections are created, set the “Use Sections” option to “No”.
Now empty your regular content area, and click the “Send Sections to Default Editor” button.
This will send all of your section content to the regular editor.
Now set “Use Sections” back to “Yes”, and save the page.
That should allow the page to be searched.
Let me know 🙂