Your interpretation has some problems. First of all Jesus used the phrase "my words are spirit" and "the flesh profiteth nothing" in the same conversation that they were talking about "eating His flesh". The focus at that point was His statement "eat my flesh". Why would you inject your statement "Flesh also means our carnal desires" into that conversation? The inference is not in that passage. Nor is it pertinent to that conversation.
>>The Protestant error is that here Jesus is discrediting the Eucharist as His body. This is not true because if Christ's flesh had profited us nothing, He would never have taken flesh for us nor died in the flesh for us.<<
Once again you inject an inference not found in the conversation. Jesus wasn't discrediting the "remembrance of Him". Throughout scripture we see that "eating the word" refers to learning and internalizing His word. Ezekiel, Jeremiah, and John were all told to "eat the scroll". They didn't physically eat the paper. Nor was Jesus talking about eating His physical flesh.