Even though you might have not have any legal recourse (RE: your H coming over) I think it would be perfectly acceptable to simply ask him not to.
H: Since you have chosen to no longer live in our home I would appreciate it if you would not come over unannounced. In the future I ask you contact me before you simply stop by.
It is hardly outlandish to ask somebody who no longer lives in the home to call/text/e-mail their desire to come over before they just pop on by. IMO if you phrase it this way you are not telling him he can't come over. You are ASKING him not to without advance notice.
Now that you have concrete proof your H is engaging in prostitution I would divide the bank accounts ASAP. IMO you are very, very foolish not to (sorry, I am not being ugly but now that we have new information it is a necessary action). Prostitutes and ethics don't really go hand in hand. How do you know a prostitute won't steal money from your H (which in turn is stealing from you?).
And yes, pack his things (neatly, just as you would want your things packed) and let him know his personal belongings are ready to be picked up.
I understand your concern about doing too much too fast but sometimes we have to base actions on the most current information. Your H is contacting prostitutes from YOUR HOME and based on the e-mails you have he very well might be planning to bring them to YOUR home. IMO there is nothing left to do but take swift action.
And really, think about it the "other way". Your H had no issue with doing too much too fast. In a matter of weeks he left you, moved out and is now planning to use the home you both shared as a rendezvous spot for prostitutes. All of that is pretty quick, no?
My attny once told me you can ask your H to do anything you want. Ask him to stand on his head for 15 minutes each day if that is what you choose. His point was you can ask the WAS to do something (in your case not come over as he pleases even though the law says it is okay) as a courtesy. If your H says no, I will not honor your request, well, okay. Legally there is nothing you can do. But you can ask.
