I would not really call myself a Calvinist as I don’t believe in things like limited atonement and perseverance of the elect is really a useless truism if you define the elect as the ones who will be with Jesus in Heaven. However I don’t discount everything he taught. I would also note that he indicates that Eucharist is beyond his ability to give an adequate explanation and I agree it is beyond anyone’s ability. That is why the sacraments were called mysteries in the early church.
I think that his thoughts on the Lord’s Supper make the most sense when considering what Jesus says. I want to give meaning to all of His words and not just the ones I choose to.
Now whatever is said elsewhere in the Bible in John 6 Jesus says
I have never heard anyone who can explain how Jesus’ statement here can be reconciled with something like transubstantiation. By saying that the elements are actually transformed into Jesus it would mean anyone receiving them would have eternal life no matter what they believe. That they should not receive does not someone from going to a parish and partaking. Would he be questioned or would he be disbelieved if he lied and said he was Catholic. By receiving he would be eating Jesus’ flesh and drinking His blood and according to Jesus unequivocal statement he has eternal life. Either Jesus is lying, which is impossible, He must mean something other than He is actually physically present in the sacrament. The only solution I see is some kind of receptionist view and a spiritual presence rather than a physical presence makes it possible to accept everything Jesus says.
A receptionist Eucharist appears to have support in the early church.
Augustine (Tractates on the Gospel of John. Tractate 26
newadvent.org/fathers/1701026.htm
Ephrem the Syrian (Memra for the Fifth Day of the Great Week (Holy Thursday), Sermon 4) Joel C. Elowsky, ed., Ancient Christian Commentary on Scripture, New Testament IVa John 1-10, (Downers Grove: InterVarsity Press, 2006), p. 236.)