Also, check to make sure there are no leaks in the roof or any moisture getting into the home due to siding or roof issues. 

Moisture intrusion is the worst enemy in housing....

you can buy penetrating sealer and surface sealer for concrete that will spray out of a regular paint sprayer.

You can put the moisture barrier in for very minimal expense.

Plus lady bugs are not nearly as bad as other things that can penetrate the walls.

What caused it in the first place needs to be resolved and that is moisture. 

No matter what your efforts, unless you completely seal the floors from each other with no penetrations, you will likely fall short of your intentions.

If that is all staining from smoke, and it's managed to penetrate or alter the glazing, it's unlikely you will achieve matching tiles.There's a good chance you will not be able to simply clean/seal/paint the walls and ceiling either ... oh, sure, for the short term it will work, but the resins will come back to the surface with time.

Looks like there's a lot of moisture in there.

Also, you could consider putting down some landscaping with wood chips or something to regulate you moisture level under the house.