> Well, if you want to be pedantic, velocity is a rate too, is it not?

Yes, but expansion is velocity over distance, so it’s not units of velocity and thus isn’t c or below or above c.

> Suffice it to say, the size of the universe expanded from the planck length to a factor on the order of 1028 in an extremely short amount of time

The observable universe. Maybe, yes, but that doesn’t make it expand at a certain velocity unless you measure over a certain distance. And at this distance, relative velocity wouldn’t be well defined due to the curvature of spacetime, and wouldn’t be constrained to c anyway.

See first answer to this: https://physics.stackexchange.com/questions/400457/what-does-general-relativity-say-about-the-relative-velocities-of-objects-that-a