In terms of seeds, it's worth remembering that they have "used up" all the seeds for star systems as they have created a system for each 64 bit integer.
What's less clear, and what we're all really talking about, is how they have spread those seeds out in 3d space versus what those seeds create.
They have said there is a sense of progression as you move into the middle, and also that things get weirder and tougher as you move in.
That means there must be a link between where the seed number (star system) is located in the galaxy and what that seed will generate. This means part of the seed must be used to set distance from centre, and also "weirdness".
So coming back to universe versus galaxy, it really depends on whether they could figure out a way to do multiple versions of these orderings. They would need to somehow distinguish a subset of the seeds, enough, so that they generated systems that felt like a separate galaxy, as opposed to just a separate system.
Imagine you have to take the numbers 1 to 400 million and they make galaxy 1, then 400,000,001 to 800m make galaxy 2 etc...if you want galaxy 2 to look and feel different to galaxy 1 then you'd need something very fundamental to happen when the seeds switch. Quite possibly different art assets and creature types.
I think this would just be too hard.
Thinking about it some more they could order galaxies with the same "weirdness" filter as systems but this post is already too long and people won't read it