Perhaps a short sermon explaining the meaning and purpose of the Lord's Supper followed by a discussion if any of the communicants are still unsure about anything. Then everyone could pray to God individually and silently (rather than have the priestly pastor act as a prayer mouthpiece to God for the entire congregation). But these are only suggestions, they cannot be mandated.
If the communicants have not previously discussed the meaning and purpose of the Supper with the stewards of the mysteries and examined themselves beforehand, they are unprepared and should not receive the Supper. Any human prayer prior to the Supper creates the very mediatorial invocation you condemn.
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This do" includes everything that is mentioned in the passages containing "This do" and nothing else. And if you read the passages where "This do" refers to the action of the Lord's Supper, you will see that there is no mention of anyone playing a ministerial role other than Jesus Christ. Unless you think that church elders stand in the place of Christ, then your statement is not supported by the passages containing "This do."
The elder, as steward of the mysteries, does stand in the place of Christ but not in any mediatorial sense. When the elder announces the grace of Christ in the stead and by the command of the Lord, the congregation should receive the spoken word as a voice from heaven.