Well it looks like this question about T in Madagascar just answered itself. Madagascarian men are a composite of three populations:
1) Austronesian O1a2 and O2a1
2) Middle Eastern J1 and T, with a pinch of R1a and J2b for seasoning, and a lone E1b1b sample.
3) Black African B2a, E1b1a and E2b
Their maternal side is overwhelmingly Black African and Southeast Asian though. No Middle Eastern mtDNA.
Note that J1 and T (and the single E1b1b) were found together in Anteoni, where there was hardly any Black African Y-DNA. Black African lineages were found in Ampanabaka, where there was no E1b1b, J1 or T.
Interestingly R1a and J2b are found mostly in Antaloatra, and are completely absent from Anteoni. So they might not have come with the J1 and T1 migration, but probably much later. If medieval Omani had brought J1 and T1, they would already have had R1a and J2b with them too (and vice versa). Therefore, based on this data, it would seem that J1 and T1 reached Madagascar before the Indo-Europeans brought R1a and J2b to the Arabian peninsula during the Late Bronze Age.
J1 is thought to have migrated from the Fertile Crescent to East Africa, Yemen and Oman some 9000 years ago, with pre-pottery herders-hunters. T1 might well have accompanied it, since both are common in the Zagros region. If J1 and T1 reached Madagascar before the Iranian invasions of the Middle East, there is a good chance that they spread all the way to the Horn of Africa, then to Madagascar in one go. Given that female lineages in Madagascar are all L (except for the Southeast Asian ones), it appears that J1 and T Neolithic herders took local wives as they advanced. The same is supposed to have happened with R1b-V88 cattle herders from the Levant to the Sudan and the Sahel (Hausa and Fula people, who have higher percentages of R1b-V88 but only mtDNA L).
This is the best hint so far that African T1 originated in the Middle East and spread alongside J1 during the Early Neolithic, but that E1b1b was probably not part of this migration. This would imply that the original Sumerians could really have been an admixture of J1 and T.
Note that the Black African B2a, E1b1a and E2b are now all found at low frequencies in the Arabian peninsula. These would have been the slaves brought by the medieval Arabs from Africa.