In regards to a large floor, there's not many more options than breaking up. I would also see what I can do with the bake map in photoshop. One cheat, might be to render the 2048X2048 size. Open it up in photoshop, reduce down the size and blur it slightly. This might muddy bake but it's worth trying.
You should be able to maintain the color of the light when baking a lightmap. What sort of lighting method are you going with? Have you tried exxagerating the light's color to see if it works? I've run a couple of test bakes and they all seem to keep the lights color.
https://www.dropbox.com/s/s30g6si9h9ahdxi/lighttest.jpg
You can see here that I took a piece of grey geometry, took. 3 different lights, baked and exported.
Complete maps are usually good for objects or scenes with details (solid white walls, etc). It's not ideal with large scenes either. If you're working with textures that have a lot of details (wood grains, lettering, metals) you're better off using lightmaps.