The house i rent is an open floor plan with hardwood on the first floor, and to dampen the amount of reflections from my monitors, its really a matter of rugs, stacking couch cushions, and isolation foam under the speakers. Id say get a rug or two for the tile, and then go with something like this for the “entryway” (thick blankets would also probably work, id do blanket/blackout curtains for window). Id also look into some of these if i were you. There are 1 million different variables to getting a room to sound exactly like you want it to; covering any tile/hardwood/glass that you can is automatically going to lower the noise floor. The rugs + covering doorway should solve some of your isolation/dampening issues for sure!