Here are a couple of things to think about. First, I grant that there can be a time and a place for a more solemn, subdued administration of the Supper. Depending on what's happening in the congregation, it may be appropriate given what is happening in the life of the congregation that week. The church may have a more subdued experience at the Table immediately after the death of a prominent member, or the excommunication of a brother or sister, or perhaps anytime when the congregation as a whole needs to mourn or repent. The first time the Corinthian church came together for the Lord's Supper after Paul's letter was read to the congregation probably wasn't the most joyful experience. I don't have a problem with occasional solemn communion services. At least once a year on Maunday Thursday the Supper should probably be experienced as such.
Second, "proclaiming the Lord's death" is not the same thing as mourning his death, or worse, attempting to relive the circumstances of his death. "Proclaiming the Lord's death" could mean one of two things. On the one hand, it could be a reference to the fact that the Good News of Jesus' death is proclaimed every time we eat the bread and drink the wine. The Supper is a public enactment of the application of the death of Jesus to the people of God. The fact that the "proclaiming" happens "as you eat this bread and drink the cup," means it's not a representation or reenactment of the death of Jesus. Eating and drinking cannot possibly be considered symbolic reenactments of death. Eating and drinking are about life and living!
The death of Jesus has happened. It's in the past. We come to the Table where the bread and wine are already there. The body and blood are separated, which means that the death has occurred. In the OT sacraficial system, the blood always had to be separated from the body of the animal, and that separation signaled the death of the victim. We come to the Table that has been spread for us because Jesus has already died. We now enjoy the fruits of his death. The death of Jesus cannot be reenacted at the Table. We can only enjoy the results of the death of Jesus—his body and blood given to us as food. Once again, it's a Table, not a tomb.
Third, the other interpretation of 1 Cor. 1:26 is the one I favor. The Lord's Supper is a covenant memorial meal. By means of the Supper the church memorializes the death of Jesus to the Father. When understood against the backdrop of the Old Testament "memorials," this New Covenant memorial meal is a dramatized ritual prayer reminding God of His covenant. The Lord’s Supper is the New Covenant memorial rite. It is the fulfillment of all the older ways that the Lord instituted as the means whereby His people would call upon His Name and dramatically ask Him to remember His covenant. All the memorials of the old order are now fulfilled and completed (compacted) into one simple covenantal memorial meal. Jesus says, “Do this as my memorial.”
At the Table we memorialize the death of Jesus. This is not about our "remembering" but about the church's reminding God of his covenant promises. It's about our action toward God. This is our prayer to God to remember Jesus and keep His covenant. We "show forth the Lord's death" to the Father asking Him to keep His gracious promises to us in Christ. In the case of the Lord’s Supper this memorializing is an act of the congregation, a pleading of the promises of God. This comes to focus in the prayers of thanksgiving (Greek: eucharist) and memorial before the bread and wine are distributed and eaten, but it is not limited to this. Indeed, the entire meal shows forth the death of Christ, as Paul says in 1 Cor. 11:26: as often as we eat and drink, we show forth the death of Christ.
This “proclamation” is not limited to the prayer or the breaking of the bread, but we memorialize Christ to the Father by means of the common meal. Here is the memorial of Your Son’s atoning sacrifice for us, O Lord, remember and be gracious towards us. Traditionally these prayers always included a summary of the life and work of Jesus Christ. A eucharistic memorial prayer should sound something like this:
It is truly appropriate and right that we should at all times and in all places give thanks to You, O Lord, our heavenly Father, almighty everlasting God. But it is especially fitting that we should now, gathered around this Table, thank You for Your gracious covenant promises to us in Christ. Remember, Father, our Lord’s humble birth, His holy life, His innocent sufferings and death, and His resurrection and ascension for us. Faithfully keep Your covenant with us for Jesus’ sake and come now to nourish and equip us for service in Your kingdom. By Your Spirit make the body and blood of our Lord life-giving nourishment for Your people; in Jesus’ Name we pray. Amen.A Eucharistic prayer like this, then, together with the doing of the Lord’s Supper “show forth the death of Jesus” (1 Cor. 11:26) to the Father. The whole meal is a dramatic prayer, a pleading of the promises to the Father by memorializing His Son’s birth, life, suffering, death, and resurrection for us.
All of this to say that our "proclaiming the Lord's Death" at the Table does not demand or imply a solemn, funereal atmosphere for the Supper. The death of Jesus should be proclaimed joyfully, whether to others (as a Gospel enactment) or to the Father (as our memorializing of Jesus work for us).