> If these each then accrete matter from the space surrounding them, they do so independently and each can accrue mass faster than a single singularity of equivalent total mass could while adhering to the Eddington limit.

The Eddington limit is a linear function of mass, so the accretion onto a collection of objects would not differ from the accretion onto a single object. At least, not because of the Eddington limit – (hydro)dynamics would play a role.

> Ultimately, this process would result in a single supermassive singularity which would be exceedingly hot, as it would be massive enough to take in matter from a much larger area than its ancestors, and would do so at a vast rate due to the matter previously being relatively untouched.

I'm not sure what object you are referring to as "hot". The accretion disks around black holes typically become _cooler_, as the black hole mass increases. And, black holes themselves are aqutally quite cold, as they do not emit significant amounts of radiation.