The sources are too scattered though, this is the problem. You make very firm and completely absolute pronouncements but the evidence is very thin, far too thin to draw any conclusions let alone absolute and total conclusions.
The sources are the unnamed source of both the Periplus of the Erythraean Sea and Ptolemy's Geographica (they clearly used the same, now lost source, probably a Greek translation of a Ximyarite guide) around the year 100.
The next source is the Islamic Caliphate records which state that the Islamic Caliphate conquered the Banaadir coast to secure its annual tribute, and record Mogadishu rebelling in the 9th century against the annual tribute. This occurred around the year 700, so there is a 600 year gap. 600 years! 600 years is an absurdly long time, the Periplus might as well not exist, you can't make connections over a 600 year gap.
After this you have Banaadir tradition stating the founding of the republic in Shingaani in 917 of the 12 leading families and the Chief Qadi ruling the town.
The next record after this is 300 years later in the last 13th century the first Sultan Fakhr ad-Diin. How did he become Sultan of Mogadishu? What happened with the Republic? Nobody knows. There are legends but they don't seem very reliable. We only know about Fakhr ad-Diin because he built a masjid which still stands. He seems to correspond with the legendary "Shirazi" dynasty, though this also seems to apply to the Republic era. Personally I think the "Shirazi" is a mythical placeholder for "the people who build Mogadishu"
After his dynasty according to various Banaadir traditions there are the Xalawaani dynasty and the Zowzaaan dynasties and then the Muzaffar. We only know more about the Muzaffar because the Abgaal also have stories about him, otherwise we wouldn't know anything at all.
Ibn Battuta visited Mogadishu in 1331, did he visit Fakhr ad-Diin's dynasty? A Xalawaani ruler? Was the ruler Zowzaan? Another, forgotten dynasty? Nobody knows!
After Ibn Battuta we have to wait 300 years before we have another historical record about Mogadishu, when we get the Abgaal story about the conquest of Mogadishu. We get name-checks of Xalawaani, no mention of Zowzaan, and we find out that Muzaffar was "from Yemen" that he "had guns" and that he was "friend of the Ajuuraan". That's all we know about him and that's the most we ever learn about him.
In the 300 year gap between Ibn Battuta and the conquest of the Abgaal a lot of things happened, but there are no available accounts of those things. Did the Ajuuraan take over? Maybe! Do we know for sure? No! Were there other dynasties? Maybe! What were their names? Nobody knows!