Please reread my disclaimer above that I’m not an expert in this topic at all and anything I write is just the way I think it’s supposed to work. (I.e. I don’t have any sources to back it up and it may very well be incorrect.)
You asked when the husband is “entitled” to a Heter Meah Rabonim. I’m not sure that “entitled” is the correct word- maybe the question should be “At what time is it appropriate for a husband to start the process”?
In any regard- if someone is trying to get the heter the way I believe it was intended to work it would be after he sent a subpoena for his wife to appear in Bais Din to initiate the Get procedure. After she refuses to come for a certain amount of time he’ll probably ask the Bais Din to write up the Get in absentia and have a message sent to her that it’s ready to be picked up.
At that point I don’t know if he’s “entitled” to the heter but he can start the process.
(I don’t believe that “entitled” is the correct word- he may very well be the cause of all the issues (and not “entitled” to a Get) and the 100 Rabonim will hopefully realize that and not sign on.)