Is there any way to set the archive period when using the auto print widget or do I have to script this?
Right.
Going for the code route.
(When in doubt, code it out) 
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I had the same request and ended up using a data directive to set the archive period for the specific report and when auto-printed.
You could also go the Upgrade Route - All the Report parameters including the Archive Code (Integer) are available in 10.1.600+
That was discussed but no desire to upgrade by this particular client (think they are tired of hearing that for everything). I did remind them that when they do decide to upgrade they have a BPM to remove.