Assuming you are using MATLAB R2022b or newer, I would recommend leveraging the LabelFormat property, which lets you specify a custom function for generating your labels.
If you set the value of LabelFormat to a function handle, then the function is called with a vector containing all the levels. You can control the output, which should be a string vector of the same size. Whatever strings are returned are used as the labels on the lines.
I don't have your raw data, so I'll give an example with made-up data.
function labels = adjustValues(vals)
% Start by assuming each label will reflect the actual value.
labels = string(vals);
% Replace -0.5 and 0.5 with -1 and 1:
labels(vals == 0.5) = "1";
labels(vals == -0.5) = "-1";
% Replace -1 to -3 with -2 to -4.
labels(vals <= -1) = string(vals(vals <= -1)-1);
% Replace 1 to 5 with 2 to 6.
labels(vals >= 1) = string(vals(vals >= 1)+1);
end
[X,Y] = meshgrid(linspace(0,pi,50));
Z = (cos(X).*sin(Y))*6;
contour(Z, [-3:-1 -0.5 0 0.5 1:5], ShowText=true, LabelFormat=@adjustValues)
