Simple Multiple Y axes with Scale, Pan, and Zoom Features

Plotting multiple signals on a line graph with separately scalable y-axes is very useful when analyzing data from data sets containing more than 2 signals (I've tried using PLOTYY or other available tools on file exchange but I wasn't fully satisfied with them so I decided to make my own)

Here is a rough script that will plot 8 scalable lines. I used the LINKAXES command to acquire a common x axes. However this command shifts most of the lines outside the white figure box and into the surrounding grey background. Is there a quick fix to my script that will scale/cut everything to the white figure box?

clear 
close all
%%Dummy data
x1 = 0:0.01:1;
x2 = x1;
x3 = x1;
x4 = x1;
x5 = x1;
x6 = x1;
x7 = x1;
x8 = x1;

y1 = x1;
y2 = x2.^2;
y3 = x3.^3;
y4 = sin(x4);
y5 = cos(x5);
y6 = -cos(x6);
y7 = -sin(x7);
y8 = x8.^4;

ylabels{1}='A'; ylabels{2}='B'; ylabels{3}='C'; ylabels{4}='D'; ylabels{5}='E'; ylabels{6}='F'; ylabels{7}='G'; ylabels{8}='H';

Create figure window

fh=figure('units','normalized',...
       'DefaultAxesXMinorTick','on','DefaultAxesYminorTick','on');
cfig = get(fh,'Color');
pos = [0.190 0.1 0.56 0.8]; %Axes Position [*left bottom *width height]
offset = pos(3)/15.5; %originally = /5.5

%Plot the first two lines
ah(1) = axes('Parent',fh,'XColor','k','YColor','b');
lh1 = line(x1,y1,'Color','b','Parent',ah(1));

lineColors = get(ah(1),'ColorOrder');

ah(2) = axes('Parent',fh);
lh2 = line(x2,y2,'Color','k','Parent',ah(2));
set(ah(2),'YAxisLocation','right','Color','none');
%Reduce width of the two axes generated by plotyy 
pos(1) = pos(1) + offset;
pos(3) = pos(3) - offset/2;
set(ah,'position',pos);  

%Determine the position of the rest of axes (spacing between
%y-axis(offset*#))
pos4=[pos(1) pos(2) pos(3)+offset pos(4)];
pos3=[pos(1) - offset pos(2) pos(3)+offset pos(4)];
pos6=[pos(1) pos(2) pos(3)+offset*2 pos(4)];

pos5=[pos(1) - offset*2 pos(2) pos(3)+offset*2 pos(4)];
pos8=[pos(1) pos(2) pos(3)+offset*3.2 pos(4)];
pos7=[pos(1) - offset*3.2 pos(2) pos(3)+offset*3.2 pos(4)];
%Determine the proper x-limits for the third and fourth axes
scale3 = pos3(3)/pos(3);
scale4 = pos4(3)/pos(3);
scale5 = pos5(3)/pos(3);

scale6 = pos6(3)/pos(3);
scale7 = pos7(3)/pos(3);
scale8 = pos8(3)/pos(3);

limx1 = get(ah(1),'xlim');
limx4 = [limx1(1) limx1(1)+scale4*(limx1(2)-limx1(1))];
limx3 = [limx1(2)-scale3*(limx1(2)-limx1(1)) limx1(2)];
limx6 = [limx1(1) limx1(1)+scale6*(limx1(2)-limx1(1))];

limx5 = [limx1(2)-scale5*(limx1(2)-limx1(1)) limx1(2)];
limx8 = [limx1(1) limx1(1)+scale8*(limx1(2)-limx1(1))];
limx7 = [limx1(2)-scale7*(limx1(2)-limx1(1)) limx1(2)];
%Create ax(3) & ax(4)
ah(3)=axes('Position',pos3,'box','off',...
   'Color','none','XColor','k','YColor','g',...   
   'xtick',[],'xlim',limx3,'yaxislocation','left');

ah(4) = axes('Position',pos4,'box','off',...
   'Color','none','XColor',cfig,'YColor','r',...
   'xtick',[],'xlim',limx4,'yaxislocation','right');

ah(5)=axes('Position',pos5,'box','off',...
   'Color','none','XColor','k','YColor',[1,0,.5],...   
   'xtick',[],'xlim',limx5,'yaxislocation','left');

ah(6)=axes('Position',pos6,'box','off',...
   'Color','none','XColor','k','YColor',[0,0.5,0],...   
   'xtick',[],'xlim',limx6,'yaxislocation','right');

ah(7)=axes('Position',pos7,'box','off',...
   'Color','none','XColor','k','YColor',[0.5,0.1,0],...   
   'xtick',[],'xlim',limx7,'yaxislocation','left');

ah(8)=axes('Position',pos8,'box','off',...
   'Color','none','XColor','k','YColor',[0,0.7,0.7],...   
   'xtick',[],'xlim',limx8,'yaxislocation','right');

linkaxes([ah(8) ah(7) ah(6) ah(5) ah(4) ah(3) ah(2) ah(1)],'x');  % Link to have common X axes.

lh3 = line(x3,y3,'Color','g','Parent',ah(3));
limy3=get(ah(3),'YLim');

lh4 = line(x4,y4,'Color','r','Parent',ah(4));
limy4=get(ah(4),'YLim');

lh5 = line(x5,y5,'Color',[1,0,.5],'Parent',ah(5));
limy5=get(ah(5),'YLim');

lh6 = line(x6,y6,'Color',[0,0.5,0],'Parent',ah(6));
limy6=get(ah(6),'YLim');

lh7 = line(x7,y7,'Color',[0.5,0.1,0],'Parent',ah(7));
limy7=get(ah(7),'YLim');

lh8 = line(x8,y8,'Color',[0,0.7,0.7],'Parent',ah(8));
limy8=get(ah(8),'YLim');

%Label all y-axes
set(get(ah(1),'ylabel'),'string',ylabels{1})
set(get(ah(2),'ylabel'),'string',ylabels{2})
set(get(ah(3),'ylabel'),'string',ylabels{3})
set(get(ah(4),'ylabel'),'string',ylabels{4})
set(get(ah(5),'ylabel'),'string',ylabels{5})
set(get(ah(6),'ylabel'),'string',ylabels{6})
set(get(ah(7),'ylabel'),'string',ylabels{7})
set(get(ah(8),'ylabel'),'string',ylabels{8})