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Seagrass is a silly suggestion yes - cork was for lfgss lols (but I still would !) . Seeing the plan - a single material through there would be nice. We have the same type of floor I think - concrete - bitumen - and 5 finger parquet. It’s a headache because you need to self level over the bitumen (and they need to use the right product to seal in the nasties.) I would have done marmoleum if I could have afforded it - but you could look at their click fix tile range. I guess to avoid self levelling you might be able to glue standard pine or reclaimed gym flooring down (using special bitumen compatible glue) and then sand and oil.
The benefit of wood is that it gives a little (tiny bit) of insulation for foot comfort - the slab won’t have insulation and so is cold on bare feet in winter (with tile particularly)
Cost wise that herringbone is £15o pm2 - sheet marmoleum is like £20. Self levelling will be the same and fitting could be cheaper. Tile - must be about 50 pm2 and same again for laying maybe.A simple plain tile in a grid would be good too .
Just to bring it back the the OG post, AIBU?
Or is that a fair price for what we've asked for?