Cessationism and Baptism

Huh? What's this going to be about.
Last night I became a cessationist. Cessationism is normally associated with the idea that one believes that certain works of the Holy Spirit are no longer seen in the church, but that's not my cessationism. Mine is that the apostolic era is over: there are no more apostles. So the character and purpose of the work of the Holy Spirit is different: there are no miracles of confirmation of ministry, or any need to provide particular wisdom concerning Christ because it's all there in the Scriptures. So He carries on doing much, including many miracles, but they are different in character and purpose: healing for the sake of a sick person, rather than frequent, public and dramatic healing to draw attention to the apostle in whose words and person the ministry of Christ is continued.
You see, my acceptance of cessationism came from a new understanding of what it means.
Baptism?
Baptism is an outward sign of those actions God purposes covenantally to pursue with an individual, placing them under obligations vis-a-vis Himself. I was caught up in the fear of either a Catholic or Zwinglian view, partly because I hadn't got the covenantal element of Reformed thinking. Yes, the invisible church is constituted by new birth, but neither the old or the new covenant visible community is co-extensive with the invisible true body of the elect. Rather, the sign of the covenant is applied to show that someone is entering a community that lives under that covenant. Can babies receive it? Well, if their parents are bringing them up in full awareness of the covenant, why might they not receive the sign of that?
Again, a new understanding brings a new view, here on paedobaptism.
Help! I'm thinking aloud and online! Any advice?