Good idea. You might want to ask her why she wants custody and try to be as nice as you can be until the papers are signed. Then if the judge sees you have tried, maybe it will clarify the custody issue better.
That's what I think I'm going to do. Three nice e-mails, offering to give him what he wants in terms of the settlement (which is more than I think he should have, but its worth it to me to get out of this). I've received nasty, explosive e-mails back about wanting "war", and so if it gets ugly, I'll have that in writing, and I'm going to ask for attorney fees as part of the settlement...to show it was him being vindictive and not because he wasn't getting a fair deal.
I feel like that old camp song about Bunny Foo Foo---I'll give you THREE chances and if you don't be good, I'll turn you into a goon!