The New Covenant is about Christ’s relationship is with His Bride, the church, of which you are a member.
I see it this way: The character of a community is the totality of the character of its individual members. i.e. if there are lots of individual moral families in a community, it will be more moral than one that has few moral families. The Jesus of the New Covenant has a relationship individually with each member of the body, resulting in a healthy “whole” body.
It’s like a “bottom up” approach rather than a “top down” approach. So, just as the Old Covenant dealt with a group called Israel and the New Covenant deals with a group called the Church, the former deals very much with the group, and members are blessed, while the latter deals with the individual members, one on one, and the group is blessed. In both cases the member are blessed, of course.
It seems subtle, but it is really huge. With Christianity, God is VERY PERSONAL, as if you were the only human alive. In the Old Covenant, it’s not nearly as personal. It’s why it is so much better.
Ps. 131.
Pretty personal.
Not really a counter-argument. An adumbration.
This approach doesn't quite seem to match up with Scripture. Take look at 1 Cor. 12, from which verses 12, 13, and 14 contradict your hypothesis:
12 For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ.
13 For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit.
14 For the body is not one member, but many.
The whole chapter follows in the same vein, and quite firmly.
If this doesn't make sense to you, there's not much value in further debating the point of trying to practice the rite of communion apart from the other communicants, is there?