Is it permissible for the Imam to supplicate with "Indeed, my prayer and my rites... until he says: I am of the Muslims" while distorting the verse?

There is no harm in the Imam's saying "and I am among the Muslims" in his supplication. It is not a recitation of a verse such that it could be said he altered its wording. The Prophet, peace and blessings be upon him, was reported to have used this very wording in his opening supplication, as narrated by Muslim in his Sahih. Both are permissible ("and I am among the Muslims" and "and I am the first of the Muslims"). Whichever of the two a Muslim uses in supplication, there is no harm upon him.