Lately, the LCMS has moved toward the Presbyterian model of the WCF but not in good way. The synod has begun to interfere with faithful local congregations while, at the same time, ignoring unfaithful congregations.
This is contrary to official LCMS teachings which specifically deny that a synod is or can be a form of church government. All churchly authority is invested in the local congregation (Walther's Theses on the Church).
Among Lutherans, there are other definitions of synod. The ELCA has synods but it is essentially episcopal (in Apostolic Succession via the ECUSA). The WELS teaches that synod is or can be church but it gives each congregation full autonomy.
If Presbyterians believe that synods may exercise church government over local congregations, I would be very much interested in the scriptural support.