Yes, shared custody=shared residency. The only requirement is that you share time equally or nearly equally. In my experience the court will order whatever has been regularly occurring rather than what is currently ordered, so that should work out.
If she does not agree to change custody/parenting time to shared 50/50, then it is possible she could request an evidentiary hearing (small trial). These can get expensive. Custody issues are considered large matters and get drug through the courts. But, don't let that discourage you. Sometimes parents come to terms with things as court progresses.
The reason I ask about the agreement is because once she figures out that she will not only get no child support, but will have to pay you support, she may elect not to agree to the change. It would be a financially driven decision, but a disagreement means court time and more $ paid to keep your attorney and judges employed. If it were me, I would keep the child support and custody issues completely separate. Get custody changed first, then take up the child support issue later.