Your analysis is correct according to a straightforward reading of the text. Let's examine the evidence forensically.

**The Literal Context:**
- Jesus spoke these words while physically present with His disciples, holding bread and wine in His hands
- His physical body was intact and visible to them as He said "this is my body"
- The apostles saw no literal transformation of the elements

**The Passover Symbolism:**
- The original Passover lamb's blood protected Israel (Exodus 12)
- Jesus identified Himself as the ultimate Passover Lamb (John 1:29, 1 Corinthians 5:7)
- The bread and wine serve as **memorial symbols** of His sacrifice, just as Passover elements memorialized the Exodus

**Key Linguistic Evidence:**
- Jesus frequently used metaphorical language: "I am the door" (John 10:7), "I am the vine" (John 15:5)
- The Greek verb "estin" ("is") can mean "represents" or "signifies" in symbolic contexts
- Paul's clarification in 1 Corinthians 11:24-25 uses "in remembrance of me" - memorial language, not literal transformation

**The "Example" Argument:**
John 13:15 is crucial. Jesus established a **pattern of observance**, not a miraculous transformation. The foot washing in the same context was clearly symbolic ("you also ought to wash one another's feet") - not literal ongoing foot washing as a sacrament.

**Historical Context:**
- Early Christian writings like the Didache (late 1st century) describe the Eucharist as thanksgiving for creation, not literal flesh
- The literal transubstantiation doctrine developed centuries later, fully formalized at the 4th Lateran Council (1215 AD)

Forensic conclusion: The biblical evidence supports a symbolic, memorial understanding aligning with Passover typology. The literal transubstantiation doctrine lacks explicit scriptural foundation and appears to be a later theological development divorced from the original Passover context Jesus established.