Legend outside plot does not work with plotyy in O

I am trying to create a plot in Octave (using v4.4.1 on Windows) using plotyy and putting the legend outside the plot (because the data covers all the usable space inside the graph). The following MVCE should reproduce the issue fairly well:

% Generate some random data to reproduce the issue
data = rand(1000,10);
data(:,1:8) = data(:,1:8)-0.5;
data(:,9:10) = data(:,9:10)+30;
timedate = linspace(737310,737313,size(data,1));
data_labels={'1';'2';'3';'4';'5';'6';'7';'8';'9';'10'};

% Plot the data
figure('Name','MVCE','Position',[300 200 1000 600])
[ax,h1,h2] = plotyy(timedate,data(:,1:8),timedate,data(:,9:10));
set(h2,'Visible','on'); 
datetick(ax(1),'x','HH:MM:SS')
datetick(ax(2),'x','HH:MM:SS')
ylim(ax(1),[-1 1])
ylim(ax(2),[20 50])
xlabel('Date & time')
ylabel(ax(1),'Something')
ylabel(ax(2),'Something else')
title('plotyy graph with legend problem')
[hl,hlo] = legend([h1;h2],data_labels,'location','eastoutside');
grid on

This the output of the code using the gnuplot graphics toolkit:

As you can see, the legend does not go outside the plot, and the second y axis is not visible (it looks like part of the plot is actually truncated).

I have tried using the qt and fltk graphics toolkits, which give issues of their own:

With qt graphics toolkit

With fltk graphics toolkit

Can anoybody suggest a fix or at least workaround? Does the same issue also happen in MATLAB or is it Octave-specific?

EDIT Using the suggestion in Tasos' answer, I managed to almost make it work with gnuplot:

% Plot the data
figure('Name','MVCE','Position',[300 200 1000 600])
[ax,h1,h2] = plotyy(timedate,data(:,1:8),timedate,data(:,9:10));
set(h2,'Visible','on'); 
datetick(ax(1),'x','HH:MM:SS')
datetick(ax(2),'x','HH:MM:SS')
ylim(ax(1),[-1 1])
ylim(ax(2),[20 50])

ax1Pos = get(ax(1), 'position');   
ax2Pos = get(ax(2), 'position');
ax1Pos(3) = ax1Pos(3) * 0.73;      
ax2Pos(3) = ax2Pos(3) * 0.73;
set(ax(1), 'position', ax2Pos);    
set(ax(2), 'position', ax2Pos);

xlabel('Date & time')
ylabel(ax(1),'Something')
ylabel(ax(2),'Something else')
title('plotyy graph with legend problem')
[hl,hlo] = legend([h1;h2],data_labels,'location','eastoutside');
pos = get(hl,'Position');
pos(1) = 0.9;
set(hl,'Position',pos)
grid on

Which produces:

Apart from the fact that the legend overlays with the second y axis label (which it doesn't on my screen, only when printing to jpg), the problem is that Octave appears to plot two legends on top of each other for some reason: one with the first set of data attached to the first set of axes, and one with the complete set of data, for both axes right on top of the first legend. This is obviously wrong, and trying to set the Visible property of hl to off deletes both legends, not just the one.

UPDATED: deals with both legend placement and OpenGL precision affecting graph.

Regarding the problem of the legend not appearing exactly in the position you want it to, you can manually adjust the position of all axes involved in a figure, to place them exactly where you want.

Regarding the problem of OpenGL being unable to deal with the precision involved when adding small numbers to a large number, plot the graph with only the small numbers involved, and then simply adjust the xticklabels to correspond to the numbers you desire.

Full code below:

% Generate some random data to reproduce the issue
data = rand(1000,10);
data(:,1:8) = data(:,1:8)-0.5;
data(:,9:10) = data(:,9:10)+30;
t_offset = 737310;
timedate = linspace(0,3,size(data,1));
data_labels={'1';'2';'3';'4';'5';'6';'7';'8';'9';'10'};

% Plot the data
figure('Name','MVCE','Position',[300 200 1000 600])
[ax,h1,h2] = plotyy(timedate,data(:,1:8),timedate,data(:,9:10));
set(h2,'Visible','on'); 
ylim(ax(1),[-1 1])
ylim(ax(2),[20 50])
ylabel(ax(1),'Something')
ylabel(ax(2),'Something else')
title('plotyy graph with legend problem')
[hl,hlo] = legend([h1;h2],data_labels,'location','eastoutside');
set(hl, 'position', get(hl, 'position') .* [0.975, 1, 0.975, 1] )
grid on

ax1Pos = get(ax(1), 'position');   ax2Pos = get(ax(2), 'position');
ax1Pos(3) = ax1Pos(3) * 0.95;      ax2Pos(3) = ax2Pos(3) * 0.95;
set(ax(1), 'position', ax2Pos);    set(ax(2), 'position', ax2Pos);
XTicks = get(ax(1), 'xtick');
set(ax(1), 'xticklabel', datestr(XTicks + t_offset, 'HH:MM:SS'))
xlabel('Date & time')
set(ax(2), 'xtick', []);

Output: