Here is a first draft of how the first part of the Service of the Table might go in a liturgy drawn strictly from the language of Hebrews:
Do not neglect to do good and to share what you have,
for such sacrifices are pleasing to God. (Heb 13:16).
Invitation to the Lord’s Table
Brothers and sisters,
since we have confidence to enter the sanctuary
by the blood of Jesus,
by the new and living way
that he opened for us through the curtain
(that is, through his flesh),
and since we have a great priest over the house of God,
let us approach with a true heart
in full assurance of faith,
with our hearts sprinkled clean from an evil conscience
and our bodies washed with pure water.
Let us hold fast to the confession of our hope without wavering,
for he who has promised is faithful. (Heb 10:19-23)
Grace be with all of you. (Heb 13:25)
And also with you.
Let us approach with a true heart in full assurance of faith.
With our hearts sprinkled clean from an evil conscience
and our bodies washed with pure water. (Heb 10:22)
Let us hold fast to the confession of our hope without wavering.
For he who has promised is faithful. (Heb 10:23)
The Prayer of Thanksgiving
It is fitting that we should have such a high priest,
holy, blameless, undefiled, separated from sinners,
and exalted above the heavens. (Heb 7:26)
Your throne, O Christ, is forever and ever,
and the righteous scepter is the scepter of your kingdom.
You have loved righteousness and hated wickedness;
therefore God has anointed you
with the oil of gladness beyond your companions. (Heb 1:8-9)
(The Sanctus hymn may be inserted here.)
In the beginning, Lord, you founded the earth,
and the heavens are the work of your hands;
they will perish, but you remain;
they will all wear out like clothing;
like a cloak you will roll them up,
and like clothing they will be changed.
But you are the same,
and your years will never end. (Heb 1:10-12)
You are a priest forever,
according to the order of Melchizedek.
Therefore, you have become the guarantee of a better covenant.
You hold your priesthood permanently,
because you continues forever.
Consequently you are able for all time
to save those who approach God through you,
since you live forever to make intercession for us. (Heb 7:21-25)
When you came into the world, you said,
“Sacrifices and offerings you have not desired,
but a body you have prepared for me;
in burnt offerings and sin offerings you have taken no pleasure.
See, God, I have come to do your will, O God.” (Heb 10:5-7)
(The Institution Narrative may be inserted here.)
After you came as a high priest
of the good things that have come,
then through the greater and perfect tent
you entered once for all into the Holy Place,
not with the blood of goats and calves but with your own blood,
thus obtaining eternal redemption.
May the eternal Spirit,
through whom you offered yourself
without blemish to God
rest upon this offering of bread and wine,
and may your precious blood
purify our conscience from dead works
to worship the living God! (Heb 9:11-12, 14)
The Eucharistic Prayer is probably the most problematic text in the liturgy because different communions have different standards as to what should be included and how it should be phrased. The proposed text cleaves closely to the actual language of the book of Hebrews, and thus does not include an Institution Narrative (although there is a pretty good place where one could be inserted, as I’ve indicated). Also, it seemed most fruitful to cast the entire prayer as addressed to Jesus. It thus comes across vaguely “East Syrian” in form.
A Sanctus would easily in the location I have indicated (perhaps introduced with language reflecting Heb 1:6). I would also suggest that theologically appropriate elaborations on the Epiclesis could be inserted if desired between “…this offering of bread and wine” and “and may your precious blood….”
I don’t like that Heb 10:22 features in both the Invitation to the Lord’s Table and the Opening Dialogue, which in itself is a good argument for sticking with the traditional Sursum Corda. Still, I’ve provided the alternative texts in case somebody can propose something better.