Marc, you are running into the situation many of us have run into: many AVR libraries used AVR specific techniques to squeeze capability & speed out of the platform and they do not translate well to the Due or other platforms.The forum here has some posts that are very good for specific situations but no one has compiled a comprehensive "how-to" (maybe we've left that to our good friend Marc?)
The timer library posted in the libraries section in this forum appears to be rather good (insulates one from the chip registers) - you could use that to generate an even every second to do a clock or counter etc.
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