Joseph - you could perhaps try changing the parent property of the stored graphics object to be that of the new parent axis. For example, we can create a recrtangle object on one figure
>> figure
>> axis([0 10 0 10])
>> hRect = rectangle('Position',[1 2 5 6]);
and then "transfer" this rectangle to another figure
>> figure
>> axis([0 10 0 10])
>> set(hRect, 'Parent', gca);
Perhaps this will work for you too.
