What in specific lines up with Ibrahim Ja'al being an Abbasi? And I'd rather stray away from oral traditions knowing the history of Genealogical folklore among Sudanese Arabs.
Yes! This is exactly what I and Jay Spaulding are trying to make clear. It is totally ridiculous for us to believe that all Arab tribes descend from the Arab nobility they claim to descend from, given this Spaulding maintains a high level of skepticism when approaching claims like these to provide as accurate an understanding as possible. I certainly think some Arab tribes have individuals who will have some Abbasid Lineage, this is inevitable but I definitely do not imagine the frequency to be anything near to what is claimed by Sudanese people. We can never be sure how many people are actually of Abbasid lineage but we know for sure it's very plausible to believe it's nowhere near 80% and up of Sudanese Arabs.
Even Spaulding acknowledges that it would take literally one Abbasi having children in the region to have more or less every Sudani have some degree of Abbasi heritage. On the topic of Ibrahim Ja'al, every single Arab tribe in the Sudan unanimously agrees that he was an Abbasi, Ibrahim Ja'al himself was very wealthy - which would track with a chief of the vaunted Abbasi tribe, various Arab contemporary sources state that several tribes of Quraysh were making their way into the Sudan such as the Banu Umayya, the obvious hostility of Fatimid authorities towards Abbasis, etc all point to Ibrahim Ja'al's lineage very likely being legitimate.