You are correct in that there is a "No Blackout Dates" policy, but some hotels limit the number of standard rooms available for redemption on a limited number of days. If you're not seeing any rooms available for the dates you've selected, then all the rooms available for purchase with points have already been taken.
More surrounding this on the Marriott site:
Oh the power of the telephone!!! Used to pull that trick out of the hat when I needed a government rate for a 11 night stay when I was working and since we stayed there all the time some 10 of us getting a short notice gov't rate was simple as dial the number and poof.....you're on a gov't rate.
Glad it worked out for you.