When I had taken all my very careful measurements last week, what I completely failed to take into consideration was the lip of the window sill. Yes the shorty bed and the chest can just squeeze side by side in the available space, but I cannot lift the lid on the chest to open it because the window sill sticks out and stops me from raising the lid a useful amount. And no, the two items will not fit side by side in the same space if I swap them around because then the width of the bed and the depth of the wall heater come into play. So after a lot of faffing I have finally concluded that this is the most aesthetically pleasing of all possible workable options. No, you can't see the lovely front of the chest this way, so I have included it in extras for you. I have also included the other end of my sofa for your amusement.

Yes, I will need to invest in a little mattress, but I checked the availability of those before committing to the purchase.