I am in a similar situation.
I live in a 1-room flat. It is actually a house with 3 floors and this "floor" was built later on. The reason I put "floor" in quotation marks is because it does not span the entire area of the house. What I mean by that is that it is connected with the rest of the house via the same stairs and corridor, but only about half of the size of the other floors. The house has a flat asphalt roof and my "flat" is covering about half of that space and the rest is still the roof.
I do not have access to the ground and cannot place my station there, so what I had to do is put the actual station on the roof.... you can probably understand now why I never really cared about the data. The wind sensor is placed above the roof, it is actually at the right height above the ground, but the problem is that I live in a city center and there are much higher buildings around so the wind is much smaller than it should be.
I have the WH1080, a very cheap station, but actually surprisingly accurate. But the problem is obvious. The roof gets very hot on sunny days, so the station temperature is way too high. No shielding would help here because the temperature it measures is in fact correct. I made my own shielding which is better than the original, but it simply gets much warmer on the roof and even if I had Davis with FARS, it would measure the same thing because that is really the temperature on the roof.
But when I now compare my data to the nearby METAR station on the airport, I was very positively surprised how accurate the measurements are. At night for example it is about 2 degrees more - but in this case this is also due to the fact that obviously the city center is warmer and the airport, which is a few km away from the town, has lower temperature. But the difference at night and on overcast days is pretty much constant. Also the pressure almost exactly matches the data from the airport.
But back to the point, in your situation, in my opinion there isnt much point in getting expensive FARS or some sophisticated shielding. If there is no way you can correctly place your station 2m above the ground and in a shadow, then even the most expensive station will not provide 100% accurate data. It will still be usable, but that few decimals difference probably wouldn't be worth the costs.