When pages are moved, it updates the time stamp on the categorylinks table. Since the category is already added to the page, it should keep the time stamp from when the category was added, not when the page was updated. (By the way, in case you didn't know already, the cl_timestamp provides the "publish date" on the various DynamicPageLists on Wikinews)
Currently, when the category is sorted by a sortkey that is NOT EQUAL to the page's title (or no sortkey is specified in the wikicode, which sorts it by the page's title), it does not update the cl_timestamp value.. so a workaround would be to explicitly specify sorting by something other than the page's title (trim off the last character of the title, random characters, whatever). For example:
Moving a page with [[Category:Foobar|Foobar]] updates cl_timestamp
Moving a page with [[Category:Foobar|Foobaz]] does NOT update cl_timestamp
Moving a page with [[Category:Foobar]] updates cl_timestamp
Moving a page with [[Category:Foobar|]] does NOT update cl_timestamp (Foobar becomes the sort key)
Moving a page with [[Category:Foobar|Foobar.]] does NOT update cl_timestamp
On line 2358 of includes/Title.php, modifying the SQL to set "cl_timestamp=cl_timestamp" will make it not update the timestamp.