Yeah, MOEs and POEs will *not* give letters of release, unfortunately, even if the actual school one works at is very understanding.
I know several people who left a contract a few weeks early to work at another, more favourable position.
They had their new place of employment post-date the start of the contract a month or so, and essentially stayed on their old visa and worked for under-the-table money until it expired and they renewed it with their new employer.
Such a shame that they got away with it!