Simple. Delay it for a few days. I would imagine MIT's administration reads the news. Even if they publicly announced a deadline, which I don't think they did; it's not like they couldn't offer a good rationale for delaying the release of the findings. My opinion hasn't changed. Given the date of release and their objection to the FOIA requests, the only things MIT really wants is to have this event forgotten and to disavow any wrongdoing on their part.
The optimal thing for MIT would have been to release it after PFC Manning gets ~20 years (which is my prediction; not found guilty on aiding the enemy, but everything else). It's weird to do something slightly shifty (morning-of) but not optimally shifty.
I would argue that would make it too obvious. Besides while it may be more optimal to release it after the verdict, releasing it in the morning on the same day has essentially the same effect.