I totally get why you want to make things look um..better. For now you can use a throw rug / runner, whichever fits best. I have attached a few that i thought would allow some tie in colors for u. Definitely replace the flooring as soon as you can. My advice is to buy a rug that you can use in another area of your home, that way the money won't go to waste. You might even want to keep using it where you put it now.

My advice would be to find a grey rectangular rug for the kitchen (confined within the grey tiles) with a border the same/similar color as the entryway tiles....Then just put a small rug or mat next to the door. If u put too many rugs it will further "stop" the eye.

I wonder who thought you needed to "break up the floor space"? You should want to have continuity and flow not a change of tile between areas.

Tear out the old and replace with new.

I am assuming this is a rental? I would get a rug that is as wide and long as you can afford/fit in the middle section and try to cover that tile. I can see MAYBE the two tiles, but 3 is too much!