I used another simple sed script to get rid of empty lines and page breaks.
After this preprocessing, I compiled to DVI and ran catdvi -s.
I don't publish the script here, since that it is really specific to my-own style and conventions.
I used a sed script to do some more fine-tuning, like adding periods to section names and description labels.
I removed line numbers using the nopageno package.
This is required so that captions won't break the paragraphs when transforming to plain text.
I arranged for all floats to hold their positions using the floats package and the H option.
I managed to do it using the following trick: Therefore, I needed to convert my LaTeX document to as plain as possible text document - Not a simple task. LanguageTool is a very nice standalone, Java-based grammar checker.