I like that answer, but isn't the Reformed idea a bit much? I am very comfortable with the idea that the Supper is real but only in a spiritual way. However, to stipulate that we are transported to heaven to be in the presence at that moment, etc. etc. is just unwarranted IMHO. It's nice in a way, almost grand, but it's without any basis that I can see.
I can definitely relate to this. The whole idea is driven by Christological concerns, namely that the Bible clearly states Jesus ascended into Heaven, is seated at the right hand of the Father, and will only come again at the final judgment. In other words, if Jesus is in Heaven, how can Jesus be here on Earth in the Lord's Supper (either spiritually or physically)? That's the concern they have. If you say, "spiritually," they'll say that now you're separating Jesus' divine and human natures (or mixing them, depending on your response). This concern has been addressed in a lot of different ways. Lutherans suggest that "the right hand of the Father" isn't really a location in the way humans normally think of it, for instance. Others, such as Eastern Orthodox, just affirm a real, local presence but say it's all a mystery. John Wesley also held to a "mystery" view, although he leaned more in the Calvinist direction on that one.
In my opinion (and I am, of course, no one important), it makes far more sense just to say, "Jesus is present, Jesus is at the right hand of the Father, and I don't know how all that works, but it does."
With that said, when you understand the underlying concern, I think the idea is more reasonable that it may appear at first glance. Also, if you read Calvin in the Institutes at length on this point (beginning with his chapter on the sacraments), what you see is that the view is much more nuanced than what you described, even though that's the view many people attribute to Calvin (including many Presbyterians). His actual position is much more careful (again, in my opinion).
I don't want to name names or point fingers, but I have been interested in this possible alternative in the past, mainly because (as I noted before) I know some Anglicans who have made that move and I consider them to be careful and conscientious. This was before you asked your question here. But when I check into the only possible choices--OPC or PCA--I find such legalisms and hair-splitting definitions, coupled with a real self-righteousness, that I'm just turned off. I'm referring to what is posted on the denominational websites.
When I have read OPC sources, that has definitely been true in my experience. PCA sources have seemed less strict and Puritanical (not that the Puritans were all bad; J.I. Packer loves them!)
I've also spent a lot of time reading/listening/watching things produced by R.C. Sproul and others affiliated with Ligonier Ministries (which is led by Sproul). They tend NOT to be the kind of nit-pickers you mentioned before. In fact, Sproul has taken heat over the years for some of his "odd" views (by Presbyterian standards). For instance, at his church in Florida, he has murals of Jesus, etc. and has openly advocated for displaying pictures of Christ (although, he says people should be very careful with how they depict him). This man is an active PCA pastor and clearly not a fundamentalist. Further, John Frame, who teaches at Reformed Theological Seminary (if I remember correctly), has spent a ton of time writing about a non-traditional view of the Regulative Principle that many Anglicans would feel more comfortable with (although, Anglo-Catholics would not).
I guess my experiences have been different than yours, and that it probably one reason I feel a little more comfortable. I think within the PCA and probably parts of the OPC, you'll get people who would be evangelical Anglicans in England, and you'll get others who are much more strict in terms of how they interpret and apply the various Reformed confessions, such as the Westminster Standards and the Three Forms of Unity.