There will be singing at St Pat's at the 1pm mass tomorrow. I am just planning it out at the moment.
The Psalm is the easy bit. Chris Willcock SJ's Psalm 51 is mandatory (cf. Psalms for Feasts and Seasons or TIS 32.)
We will use the entrance antiphon as it is in the missal, set to "Make me a channel of your peace", with the people using "You are the Lord our God" as a refrain.
During the signing with the ashes, I think I will use Michael Herry's "Give us hearts renewed" (from "Song of the Pilgrim"), which is short and repetitive. I have been looking at the "antiphons" that are suggested in the missal for singing during the signing, but I have no idea (at this point) how to sing them. Some work and research needed there. There is also a "responsory" listed, but again, no suggestion of how to use it. Mons Elliot, in his Ceremonies of the Liturgical Year, simply says that "during the imposition the antiphons or appropriate penitential hymns are sung."
I think we will use "O Lord throughout these forty days" as the communion hymn. It is possible that you do not know this hymn. It is probably more current among Lutherans than among Catholics, but there is no reason why Catholics should not sing it. And it has a common metre 18.104.22.168 so it can be sung to a whole range of tunes. Lutherans use "Caithness", but you could use "Amazing Grace" or "Crimond"--though probably not advisable. Better would be "Belair" or "Tallis' Ordinal". In fact, I think I will use the latter (TIS 397). Here is the text based on an original by Claudia F. Hernaman (d. 1898) and Gilbert E. Doan.
1. O Lord, throughout these forty days
You prayed and kept the fast;
Inspire repentance for our sin,
And free us from our past.
2. You strove with Satan, and you won;
Your faithfulness endured;
give us your strength, your skill and trust
In God's eternal Word.
3. Though parched and hungry, yet you prayed
And fixed your mind above;
So teach us to deny ourselves
Since we have known God's love.
4. Be with us through this season, Lord,
And all our earthly days,
That when the final Easter dawns,
We join in heaven's praise.