Earlier quoted context omitted.
Given that a UUID identifier fits in a single cipher block, and the whole point is that these are unique by construction (no IV needed so long as that holds true), it seems like a single round of ECB-mode AES-128 would enable quickly converting between internal/external identifiers. 128 bits -> 128 bits
Why not just use the AES-128 result as the UUID then? What's the benefit of the internal structure at all? If AES-128 is an acceptable external UUID (and likely an acceptable internal one), then you might as well just stick with a faster RNG.
Purely random identifiers are the bane of DB indices. The internal structure is sequential-ish and therefore indexes well.