hi there hows about building a pen outside your kitchen(or whatever)window,then you could open your window on a nice day to let him,and the house,have some fresh air.And he could jump outside,down some purpose made steps,and have a play,you could make this from wood so it wouldnt look tacky,put hanging baskets around it,maybe a polycarbonate roof.It would be best to use strong weld mesh 1" rather than chicken wire.

Just realised your garden is not joined to your house!!so this wouldnt work!maybe you could make like a giant rabbit run which could be folded when not in use,can it not be a permenant fixture/?