I don't really see South Arabia Indianising though.
The area has urban life, thriving trade and states for about as long as (Vedic) India and has documented writing way earlier (I'm discounting the IVC here and all the theories, very popular in India, that connect it to the Vedas. I am going with the mainstream view of Western Indologists that see a discontinuity in urban life between the IVC and Vedic phases, although I recognized that this poses some problems).
I mean that it is difficult to see what could lead Indian cultural traits to impose themselves to urbanized, literate South Arabians with the same level of prestige they had to pre-state Austronesians. The were in considerable interaction with the Hellenistic/Roman world, felt its prestige clearly and incorporated some its fashions and styles - but never considered Hellenizing or Romanizing.
It is worth noting that South Arabians exerted significant trading influence (according to the Periplus of the Erythrean Sea, actually political control) over the would-be Swahili coast. The Periplus refers to at least a city, Rhapta, that has to be in that general area in the first century AD (it is said to be ruled by "Homerites", that is, the South Arabian kingdom of Himyar - I am not aware of any idependent confirmation though, and standard work on South Arabia hardly mention rule over East Africa that far south). By the way, the name "Azania" is also from that text, so I assume it's Greek, not Persian (although I suppose it's related to the Arabic-Persian word "Zanj" indeed). This is supposedly even before Bantu speakers settled the area.
I don't how this relates to the archaeological record, but to my knowledge, not a single letter in any South Arabian script has ever been found in Africa south of Ethiopia. Which would be expected if the Himyarites actually had colonies there, I'd guess.
A problem is that this East African trade looks, overall, like it was marginal (I am talking Roman times,. The main items involved were probably ivory and ostrich feathers. Gold is also mentioned, and I've read suggestions that Rhapta was actually the sea outlet for gold from Great Zimbabwe -except that this does not seem to add up with the accepted dating for the latter IIRC.
However, I gather that India had plenty of ivory, easier ways to get gold, and ostrich feathers... you don't create a new Indianised cultural area just to get those.
But this is all about before the Bantu moved in.