Lord's Supper, water baptism, church membership, morphology and conundrems of our own making

In relation to Lord's Supper, water baptism, church membership, and morphology, some confusion arises when modern Christians try to line up competing systems with what we perceive to be biblical. Often inconsistencies are noticed within one system, so a wholesale transfer to another over-developed system will be adopted.

The execution of these things (Lord's Supper, water baptism, church membership, even morphology) in the different camps grows out of an overly-wooden and overly-developed understanding. I think some Biblically guided deconstruction would be useful...more than can be explained in this short post. But for those familiar with some of the arguments between paedo-baptists and credo-baptists, I would ask these questions.
Do you agree that Old Covenant Israel (whose male children were marked in infancy) was a people to whom the TERMS of the Old Covenant were extended?
And now, to whom are the TERMS of the New Covenant extended?
As highlighted in John 3 and several of Paul's epistles, the terms of the New Covenant are extended to the whole world. That's right the TERMS of the New Covenant belong to your neighbors children (who do not attend a church) as much as those terms belong to your children. Now, "Will they hear the Gospel and respond with faith in Jesus Christ?" is another question.
On the personal side: I try to use the Lord's Supper as an instructional time for my children and do not deny them the bread and wine anymore than I would deny them any other food (kind of passover-like). As for water-baptism, I let them under go it pretty much upon their request. As to their relationship to God, I make a charitable assumption, based on their profession of faith in Jesus Christ, that their relationship to God is on as sure a footing as my own...until they tell me they do not believe in Jesus....or reject the way of God's Spiritual Rule as lived and taught by Jesus....or in some way refuse to acknowledge and be loyal to Jesus. This is my approach after having wrestled my way through to what I think are proper understandings of the texts so often considered in reference to these topics. My approach probably reflects the realization that some of our technical issues are not worked out in the New Testament because in the New Testament they were not technical issues.
For a related post see:
http://personaldiscipleship.blogspot.com/2008/08/reading-colossians-and-asking-once.html