... if you are sure that you did not enforce a state on pins that are not broken out on the pHAT I'm not convinced your issue is of that nature. There's really is no reason you'd end up with such issues by merely toggling pin16 in any case.
Instead I'm thinking that maybe your soldering came loose (either on the pHAT or the zero header). What is the board activity like when you attempt to flash the board?
EDIT: to be sure I just tried flashing over the network through ssh, as expected that was not a concern with a couple of boards.