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In other words, Adobe Reader won't let you add text. What you need is a program that's a little more accommodating, PDF-wise. Try Foxit Reader 4.3, which allows you to add text to any PDF.
If your document has many headings, it's a good idea to add a table of contents in case it will be accessed outside Google Docs, for instance, if you export it as a PDF or EPUB document. You can even ...