I agree with most of what you wrote, but I wish you to consider two domains, a physical and a spiritual. Now Jesus did use parables and physical examples to "symbolize" heavenly/spiritual things. But, there are also other times where there is both a physical and a spiritual meaning to the same thing.
Do you believe you are born again? As Jesus explained, we are first born physically, but must be born again spiritually. He is not teaching that baptism represents/symbolizes a rebirth. He is not teaching a physical rebirth. He is teaching a spiritual rebirth.
Now apply the same to the Lord's Supper. Even though Jesus said we eat flesh in John 6:55, he clarifies it to mean a spiritual meaning in John 6:63. As John does not record the words of the Lord's Supper, it is a good bet that John 6 teaches the meaning of the Lord's Supper.
Lastly consider Jesus' words, "For where two or three gather in my name, there am I with them." You could rewrite it "Jesus is where two or three gather". Now, I just want to point out the Jesus is present spiritually, not physically. The word is does not insist equality in every characteristic of the subject. Is could mean: spiritual, physical, both spiritual and physical.
Good question. I'll try my best to summarize, but you've touched on a very complex subject, so please bear with me
We (Lutherans) certainly do distinguish between physical and spiritual, but it should be understood correctly. The Lutheran view (that I hold to) is that the Eucharist is a Holy Mystery expressed as Sacramental Union. This means that the bread, being ordinary bread, is consumed in an ordinary and bodily way. But, in, with and under the bread, there is a spiritual eating of the true body of Christ. This rests on the institution, command and promise of God. Likewise, in Baptism, the water is regular water, but by the word and promise of Christ, they are joined together and form a Sacrament. viz a Holy Baptism into the name of the Father, the Son and the Holy Spirit, through faith. It's not a work that we do, but a gift from God; a means of grace.
When I say "spiritual", what is meant is divine and incomprehensible; something only rightly apprehended through faith. I don't mean "spiritual" in the sense that's not substantially real or symbolic, because it is the true body and true blood of Christ given for us. (It is not Consubstantiation, although Lutherans are often accused of this)
I don't know what your teachings are on the Eucharist, but IF it's in line with Calvin, then I would perhaps summarize it thus: Lutherans confess that Christ is present in the Eucharist and that the bread and the wine are channels or means of grace. This is a bit different from the Calvinistic school of thought, that makes the Holy Spirit an intermediary person, making the Real Presence somewhat indirectly, yet real (and arguably direct, given God's oneness - though it can be viewed with implications). So, if we say "spiritual eating of Christ", Lutherans don't mean via the Holy Spirit, but Christ directly. Christ offered himself, and so that is who is offered. However, we also believe that the Holy Spirit is present, but in a different form; namely through God's Word, and operating within us - sanctifying, producing faith and good works.
Lutherans differ from Roman Catholic teaching in that the body of Christ is not local, but we do not mean that the body of Christ entirely absent nor by extension either. What is meant is that it's holy and mystical; Christ, being fully man and fully God, glorified and at the right hand of the Father, is both present among us and not. He's not locally present with us according to his human nature (as he was with the apostles), but he is spiritually present with us, in accordance with his human nature through the power of his divine nature. Just as the Holy Spirit can be everywhere at all times, so the Son can be everywhere at all times; that is, through his divinity. Yet, Father, Son and Holy Spirit are one. In a word, the fullness of the deity dwells in Christ and Christ offers himself in the supper, even though he reigns in heaven, and will again return (locally) on the last day.
Sorry that my answer is very long-winded, but the reason I wanted to explain this difference (even if you don't believe in a Calvinistic view or Roman view) is just so that I can more easily explain the second part of your question:
"Jesus is where two or three gather". We hold that - though closely and naturally connected - this is different from the Real Presence in the Eucharist, because this rests on a different institution and promise, to wit, the institution of the Church - that we, the believers, are the body of Christ and Christ is the head. In this respect, and through faith, new birth, and the indwelling of the Holy Spirit, Christ is with us, because we are united with Christ through faith.
I hope that helps clarify a bit, even if my description is imperfect. Should you be interested in a more accurate definition of the Lutheran doctrine on the Eucharist, I'd recommend checking out our Confessions:
The Large Catechism - Book of Concord