And what is this presumed "abrahamic covenant theology from the Arab perspective"? And who were the "Arabs"? And were there such a people who self identified as such then, or was it an identity imposed on them externally, perhaps the Romans?
In Galatians where Paul recalled his sojourn in Arabia, he wrote:
But what does the Scripture say? “Expel the slave woman and her son,
for the slave woman’s son will never share in the inheritance with the
free woman’s son.” Therefore, brothers, we are not children of the
slave woman, but of the free woman. [Gal 4:30,31]
From the antecedent context, the slave woman is Hagar, the supposed mother of the Arabs, Ishmael's offspring.
If there was an Arab perspective of the covenant, and if they believed their origins as revealed in the Scriptures, then it was clear, as it was to Paul, that they were not the inheritors to the covenantal promises. Indeed God promised Hagar that Ishamel himself shall be the father of twelve princes, but certainly not the promises of the covenant.
Unless the Arabs had a different narrative, e.g. that the promises were for the first born Ishmael and not Isaac, which, apparently, was certainly not what Paul believed, even if such a narrative was extant then, which we do not know or have any evidence for, at least not in the Scriptures.
But if you do assert that the "Scriptures" were already corrupted then, and only the "Arabs" had the authentic copies, or rather, had remembered the true stories, and that Paul became acquainted with these from his sojourn in Arabia, then these assertions are self defeating, for clearly Paul had rather stick with the "corrupted" written Scriptures, than any presumed authentic, in all likelihood, oral, "Arab" perspectives.