crazybrit
You are making a few mistakes
There is no problem to get fleishigs during the nine days. AS Dy mentioned earlier. The only thing you cant do is eat fleishigs.
You say regarding your grill that pareve cooked on it is “fleishig gomur lkol hadaos” This is certainly not true. If the grill has no meat on it even without kashering it, pareve cooked on it remains pareve (but cant be eaten WITH milk). If the grill hasnt beesn used in 24 hours not only do you not need to wait after eating your pareve sausage prior to eating cheese,but you can even put cheese on the sausage bedieved. According to most though you cant lechatchila cook the sausages on the grill planning to place cheese (though according to the biur hgra you cna even do that!).
As popa pointed out even if the grill was dirty it wouldnt make you fleishig (though this couldnt be eaten with cheese)