Doctor Strange did not need to change the initial magic spell
When Peter Parker first became Spider-Man, his Aunt May and friends did not know that he was Spider-Man right away. Doctor Strange's first spell should not have been changed for exceptions at all. Peter could have re-introduced his secret identity to Aunt May and his friends a second time, without messing up the multi-verse.
They could then all go to M.I.T. and a new adventure begins there.