You're right, NEVER enough space. I have tens of flats of seedlings outside the GH as well and at least 20 over to the farm already.
I would love a brick floor, but this one's getting mulch when I get it emptied this summer. My son bought me a used GH at his house that he put a brick floor in the aisle, pea gravel under the shelving units and in ground area across the back. And even with two GHs, still NEVER enough room!
Would love to see pictures of your inside and seedlings!