Is it permissible to conclude the supplication before the taslīm in prayer with: "Subḥān Allāh wa bi-ḥamdihi, subḥān Allāh al-ʿaẓīm, wa lā ilāha illā Allāh, wa Allāhu akbar, wa al-ḥamdu Lillāh"?

The appropriate place for supplication (du'a) is after the Tashahhud and before the Taslim (the salutation that ends the prayer). As for dhikr (remembrance of Allah), it is after the Taslim. It is best in supplication to begin by praising and lauding Allah, and sending blessings upon the Prophet ﷺ, then to make the supplication, and to conclude by praising Allah. It has been reported from some of the Salaf (pious predecessors) that they praised Allah in their supplications after the Tashahhud.