I agree with you that partaking of the bread and wine as Paul says is a proclamation of the "Lord's death until he comes."
But Paul does not say that we are proclaiming the Lord's deaths[plural]. Paul says "death"[singular] not "deaths"[plural]. The Catholic position is that Jesus is sacrificed every day at every mass at every Catholic Church on the globe which means "deaths"[plural] and a lot of them.
Paul says that we are proclaiming a single event, a single death that happened only once in history --- the Lord's death[singular] on Calvary, period.
And the words: "until he comes" follow in that same verse, even in my Catholic Family Bible, indicating clearly that Jesus is not present right there in the bread and wine. The very act of partaking of the bread and wine indicates that He is not present. His absence from our presence because of His death on Calvary is what is being proclaimed until the day when returns as He promised.
As far as "eating and drinking unworthily", it is those who demean the singular death of Jesus on Calvary and its efficacy who are eating and drinking unworthily. They are the ones who demean the value of that one death by their words and deeds to the demeaning effect that His one sacrifice was not enough to save sinners but needs to be followed up again and again day after day place after place ad infinitum without end. They are the ones who do not see the "worth" in that one singular death 2000 years ago, but continue to eat and drink unworthily. Food for thought.