You should not negotiate after you accepted the oral offer … per

Once you acceptedoral offer, the deal is sealed!  It took HR time to prepare package and get signature ... Of course they are shocked and unhappy.  Frankly if I were the HR, I would suspect your integrity and capability to make sound business decision.

Now you have to keep going on this path, and wish that there is no back up candidate.  Do not email, just call... apologizing by saying "you misunderstood the salary ... since child was crying ... " You really appreciate this offer, and appreciate HR to follow up with the manager... blah blah.