I think that this is idea is making a mountain out of a mole hill. SE clearly just wanted to reuse assets. The evidence for this is that they recolor other monsters that have nothing to do with Light intrinsically, and then tag'em as a Sin Eater and have'em appear on The First. The most recent example is the Sin Eater that Lyna wanted us to kill with her Crystarium Guard so we could motivate them. It's literally a recolored version of The Curator from The Fractal Continuum.

I mean, there's also the fact that a lot of Sin Eaters are just recolored animals that kept their overall form, but became totally corrupted by Light. The bears in Holminster Switch, the manticores, the buuz, and whatever else. It's entirely possible, given that the same races exist on all worlds, that the statues created by Amdapor were just actual creatures or automatons on The Source that are/were present on every shard. These same creatures would be present on The First, and if they were corrupted by Light in the same way that the bears and stuff were, they kept their form when they transformed into Sin Eaters.