What you propose to do is both illegal and unworkable.
When your employer sends you visa documents, they are designed to invite you exclusively to work exclusively for them. The Z-visa is not transferable.
When you arrive, your employer must produce the matching document that proves you are the person invited to work for them. Only the employer who issued the invitation has that uniquely numbered document. No match, no job.
The first school that sent you the paperwork has incurred considerable effort, and some expense, to send you that invitation. In addition, they have probably stopped interviewing candidates, and have classes scheduled in anticipation of your arrival.
It would spare the first school considerable aggravation and expense if you simply let them know you had reconsidered their offer.
Normally, I wish letter writers the best of luck, but in your case, I'll just say, "May your Karma be swift."