Actually, to sue for abandonment you have to be able to document that you have no idea where your W is or how to find her.
Since you are sharing custody and you send her support that is not the case. Abandonment does not mean she "emotionally" abandoned the marriage or you - it means she is GONE and you have no idea where.
I thought I could go this route too but it is a true abandonment like she just fell off the planet. If you have contact, her address and shared custody then that won't fly.
It will go to court for the legal separation - how it proceeds in court is the question. If you both agree your attnys simply need to put it on the oral record in chambers (you will not be there, it is closed door). If you can't agree, well, a pre-trial conference for the separation Agreement will happen.