It is in paraliturgical texts and devotions that we find the secondary Thanksgiving themes best utilized -- and here we bear in mind that popular piety, as the former Cardinal Ratzinger noted in Spirit of the Liturgy, "is the soil without which the liturgy cannot thrive."
Foley provides an illuminating citation of devotions for the day from
Bishop Camillus Paul Maes in 1913:
Carroll’s Prayer for the Church and Civil Authorities, Benediction of
the Blessed Sacrament, and the Te Deum. There are other examples.
A program “for family
and parish observance of Thanksgiving Day” that the National Catholic
Rural Life Conference put together in the mid-20th century re-echoes
some of these ideas. It called for attendance at Mass, private
recitation of the propers from the Mass of Thanksgiving (apparently in cases where the votive could not be offered), and
Archbishop Carroll’s prayer after Mass. The Rural Life devotional
also picks up very strongly on the harvest theme with the recitation of
Psalm 64:10-14: “Thou hast visited the earth and watered it, Thou hast
greatly enriched it” etc. The priest and people then alternate
recitation of the Benedicite or the Canticle of the Three Youths, a very appropriate thanksgiving for Creation from the Office of Lauds.
Mary Reed Newland, one of the mid-20th century mothers who helped bring the liturgy into the domestic Church, took yet another devotional approach to the holiday. In her book, The Year & Our Children (1956), she describes how her family typed out multiple copies of a long-form grace before and after meals that then came to serve as a special grace before Thanksgiving Dinner. Indeed, if we are to give thanks - gratia -- before each meal, then it is only natural for Americans to want to offer a gratia par excellence at American's greatest national feast.
American Catholics have long felt a need to integrate the holiday into their devotional and parish life and there are many options here that are worth investigating as the basis of new liturgical or paraliturgical texts. So while I agree with Mr. Foley's "no thanks" to the modern propers for the time being, I am nevertheless quite certain that a more liturgically appropriate solution could be devised that builds on these devotional elements to create a proper Mass of (American) Thanksgiving -- which, ironically, might be a good cause for us to break out the old votive Mass.
For examples of the devotions and paraliturgical prayers for the holiday, see the Thanksgiving devotional booklet published by Ancilla Press.