What one already has through faith and rebirth is not subsequently participated in through ritual. If it were, the ritual would be the efficacious source of whatever grace is envisioned to come through it, regardless of how carefully one may attempt to formulate the concept to make it seem otherwise. NT rituals (baptism and the Lord's Supper) are merely a symbolic and/or memorial celebration of what one already possesses--an outward sign of an inner reality possessed apart from the sign.
Paul's comparison of believers' communion in the Lord's Supper to pagans' participation in the sacrifices of idolatry goes a long way in proving the point. Pagans were participating in their altars by eating the meat sacrificed upon them, much in the same way OT saints did with their altar in Jerusalem. The basis for pagan belief was non-existent--idols are nothing and can produce no aftereffect in what is sacrificed to them--but what the pagans were doing was worship, and therefore sin. Demons were the force pulling the strings behind the scene, so even though there was nothing to idols, even less to meat sacrificed to a nothing; what pagans were doing was, nonetheless, a "joining of hands" with demons and therefore forbidden to Christians.
Rather than substantiating the thought that there is "something going on" in the elements eaten from the table, Paul's argument actually undermines it. By comparing the Lord's Supper to the nothingness of idol sacrifice, Paul locates anything substantial in such participation in the faith it betrays in the honoree rather than in the elements of that honor. The problem with eating meat one knows is sacrificed to an idol is not in any heeby-geebies in the meat, but in what it says about one's faith in the false god (really, the demon) behind it.
Our participation in the Lord's Supper is actually of a similar sort of sharing as the pagans are "experiencing" at their altars. Substantially, spiritually, it's not about the bread or wine or the eating of it--its about faith and worship. The participation of the pagan idolaters in their altars did not require any reality of presence or substance in order for it to be real participation (and incur just condemnation), the same holds true for believers and the Lord's Supper. What makes the practice is not the presence or the substance, it's the faith the participant has in the God it celebrates.
With a bit more to follow...