Craig, Will you be cleaning out the old filter in the new tank -while- you are fishless cycling (adding ammonia, testing, etc.) the new tank? Normally that is what you'd have going on. The addition of 1/3 of the mature media from the old filter and the cleaning out of that filter should both help to quickly cycle the new filter, perhaps in only a week, but you'd still want to test and confirm this, unless I'm misunderstanding your situation. The test would be whether the filter would then begin reducing 5ppm of ammonia to zero ppm ammonia and zero ppm nitrite(NO2) within 12 hours or less after the 5ppm of ammonia was added.. and repeat this for quite a number of days, to be sure.
~~waterdrop~~