When using alpha properties to visualize the intersection of graphics objects, there isn't really a way to make the intersection color independent of the contributing colors. The intersection is simply a weighted mean of the two colors.
You might be able to do something like this example, but adjusting your workflow from using fill() to building point lists for using patch() might be a bit of a hoop to jump through.
Alternatively, if you use fill(), you might be able to get better visual contrast by starting with more visually-distinct colors to begin with. Regardless of the selected colors, you could construct the legend for the overlap area without explicitly needing to:
x = [1 3 4 3 1 0];
y = [0 0 2 4 4 2];
color = [1 0 0; 0 1 0; 0 0 1];
alpha = [0.3; 0.3; 0.3];
hold on
fh(1) = fill(x,y,color(1,:),'FaceAlpha',alpha(1));
fh(2) = fill(x+2,y,color(2,:),'FaceAlpha',alpha(2));
fh(3) = fill(x+1,y+2,color(3,:),'FaceAlpha',alpha(3));
fh = fliplr(fh);
% create legend entries for intersection regions without actually generating the intersection poly directly
color12 = (color(1,:)*alpha(1) + (1-alpha(1)))*(1-alpha(2)) + color(2,:)*alpha(2);
color23 = (color(2,:)*alpha(2) + (1-alpha(2)))*(1-alpha(3)) + color(3,:)*alpha(3);
color31 = (color(3,:)*alpha(3) + (1-alpha(3)))*(1-alpha(1)) + color(1,:)*alpha(1);
color123 = ((color(1,:)*alpha(1) + (1-alpha(1)))*(1-alpha(2)) + color(2,:)*alpha(2))*(1-alpha(3)) + color(3,:)*alpha(3);
pint12 = patch('xdata',x(1)*[1 1 1],'ydata',y(2)*[1 1 1],'FaceColor',color12); % dummy objects
pint23 = patch('xdata',x(1)*[1 1 1],'ydata',y(2)*[1 1 1],'FaceColor',color23);
pint31 = patch('xdata',x(1)*[1 1 1],'ydata',y(2)*[1 1 1],'FaceColor',color31);
pint123 = patch('xdata',x(1)*[1 1 1],'ydata',y(2)*[1 1 1],'FaceColor',color123);
% set up legend
legend([fh pint12 pint23 pint31 pint123],'p1','p2','p3','p1 ∩ p2','p2 ∩ p3','p3 ∩ p1','p1 ∩ p2 ∩ p3');
