Are you not violating the contract of providing for your wife’s needs?
In this case it would be that she have the opportunity for someone else to fulfill that role because for whatever reason it did not work with you.
So in by refusing to allow your wife the respect and decency of an official divorce, are you not keeping her attached to you halachically against her will?
You already know that withholding the get goes against her will because she wants one and even is working towards the civil divorce.
To me, it sounds like it would help to be accountable to more than the Beis Din. Do you really need to wait until the Beis Din forces you to treat your wife like you care enough about her to recognize that doing this is best for her neshamah?
I pray that the Moderators approve this message. Shavua tov and may you empathize with the woman who ought to come first in your life. Thank you.