Cat, exactly why are you supposed to be doing all the D-related work? Is he unable to find mediators for some reason? If so, perhaps you can challenge his competency to make any legal decisions And, why are you talking to him on the phone about it?
This is not going to be a nice divorce. STBX has already consulted his own counsel. Consult with your own counsel, and let them handle the communication.
If you really want to go the mediator route, tell STBX *by email* that pushing you is unacceptable and that you are unwilling to lie on any legal documents, period.
I totally agree with Ian that you get to make your own choices about timing here. But keep in mind that the longer you wait, the less favorable your settlement is apt to be.
And Cat, you've got to take the emotion out of this. It is a business deal. You aren't going to get to punish STBX with it, you aren't going to be rewarded for having been the better spouse, you aren't going to get to prove how messed up he is. It is business. The emotional attacks (on both sides) aren't going to get anyone anywhere. They aren't worth your time or energy. Tell him once if he starts grilling you on your choices, "STBX, this isn't about you. This is about me and the kids and what is best for us. How it affects you or your life is not a factor in my choices right now.)
If he starts in again, simply say, "Unacceptable," and hang up the phone (which you shouldn't be on to begin with.) If he attacks you in emails, copy and paste the email, take out everything except the purely business matters, and respond to those.
And, why are you talking to him on the phone about it? 