There could be several reasons it was done so swiftly. This is all IMO. I have no information to prove this, but I think that perhaps his attorney said, this is what they are thinking. They will not give me a time deadline, but if I were you, I would not pussy foot around. I would get out while the getting is good, before someone changes their mind. So, that would explain why they had to move fast. Also, I suspect the reason they didn't want their friends knowing they were moving is that they could have called the prosecutor's office and said Hey, that guy you are supposed to be charging with bigamy is getting ready to move out of state. I would imagine they didn't want everybody knowing up front that they basically had permission to leave.
Also, it's drama for the tv show and that is always loved.