In the first part I tried to determine what was the minimum one could say about the Lord's Supper. One clear conclusion is that this is more than a symbol; that Jesus is present in some fashion during the service. But what are the characteristics and limits of this presence?
I don't know anyone who seriously argues that a church potluck is an instance of the Lord's Supper (Paul seems to be trying to distinguish the two). There seems to be no great groundswell claiming that every single morsel must be individually broken by the officiant/leader—in fact Jesus told the disciples to divide it themselves. The consecration/blessing/prayer for one part is taken as being for it all, which is both a reasonable extrapolation of the example and a practical necessity.
Clearly the blessing/consecration/prayer is for the food being served at that time, and not for any other bread that might be lying nearby—but it includes all that is intended to be served at that time, whether immediately in hand or not. This seems like a fairly obvious point, and it isn't disputed, but it represents one of the limits.
Does the presence of Jesus in the bread and wine extend beyond the ceremony? One obvious answer is yes, since He is present with His worshipers who have eaten these things in obedience to His command. But another answer is no: when all is done the leftovers are merely what they are. This is not explicitly spelled out in scripture (or there wouldn't have been arguments over the centuries!), but there seems to be a clear analogy in John:
The Spirit gives life; the flesh counts for nothing. The words I have spoken to you are spirit and they are life.
The words Jesus spoke were sounds; sounds which dissipated into heat and were gone—except where they found a hearing in human beings. They were life and spirit only insofar as they were received by men. They were not life or spirit for the wandering birds, but they are for us who do not even hear them directly anymore.
The life that comes with the words of Jesus has to come from an interaction with God, not from an extension of our ordinary bodily life. Sounds, however pleasant, don't repair broken DNA or clear up wrinkles. The interaction with God is real; just not physical. The wandering birds did not experience that interaction with God, and so for them the words were not spirit.
In the same way the mouse I mentioned last time, though it eats from the prayed-for/blessed/consecrated bread, does not interact with God or experience the presence of Jesus.
The bread and wine then do not undergo an intrinsic change, but only become Jesus body and blood in relation to the worshipers.
Perhaps this analogy is not convincing. Ask this, then: do the leftovers, since they were consecrated/set apart/made holy, remain holy?
If they are to be reused at a later ceremony, then in obedience to Paul's instructions they should be blessed again. This militates against the “permanently holy” interpretation, and suggests that adoration of the bread after the ceremony is not called for. It is of course offensive to attempt to misuse these elements, but if a hungry beggar appeared at the door after the service I do not think it would be blasphemous to offer him the food available; but only after the service, by no means during it.
My thoughts on the matter tend to study the operational rather than deciding about natures. This is partly from a personal bias in the way I analyze things, and partly because I judge the word “spiritual” to be a placeholder for things whose structure is not clear to us. We can call both angels and God “spiritual” but because one is created and the other the Creator the difference between their natures has to be profound.
How does participation unite us with Christ and with each other? I haven't a clue. It does—provided we partake in worthy manner.