In the Syriac tradition, leavened bread is used. Actually the only OO jurisdiction that uses un-leavened bread is the Armenian Church.
In the Syriac Orthodox Church, we have various Anaphoras, some of them being:
- of St. James
- of St. John Chrysostom
- of St. Philoxenus of Mabbug
- of St. Jacob of Serrugh
The most commonly used Anaphora is the shorter version of St. James as shortened by Mor Gregorious Bar 'Ebroyo, Maphriana of the East with in the Syriac Orthodox Church (refered to in the west as Gregory Bar Hebraeus). My understanding is that the prayer that you have quoted above is part of the silent prayer by the priest in the Anaphora of St. Philoxenus of Mabbug. The Anaphora that I have access to only includes the section said aloud, and does not include silent prayers by the priest. So I cannot confirm.