The guy down the road must've left the door to the shed open once too often to have lost all but one sole survivor! I'm so glad to hear he found you to give you the shed AND the surviving hen! I love happy endings. Did she blend in ok with your existing flock?
Don't underestimate raccoons or stray dogs from using their craftiness or weight to jump and push open a heavy door if it's unlocked. My DD's 60-lb dog can open their sliding patio door by jumping up on it and using her weight and paws -- and that brand new door is double paned glass and
heavy. When I visit I have to be mindful to keep it locked or the dog will work it open. I can't imagine a predator to a chicken coop would be any less able to figure a way to push open an unlocked door and raccoons figure out and fabricate their own fulcrums and tools to pry or open things that is sometimes impossible to believe for such a small creature. I think of raccoons as rural wild animals but they are multiplying in the cities so forgive me if I delight in seeing one occasionally as road-kill on our street. A single female can give birth up to 6 kits in each litter! In a suburb situation like ours they overrun the golf courses and slink out of street storm drains at night. Some get as fat as small goats. We occasionally hear them scampering across our roof at night. We keep a patio light on near the coop and will be investing in some blinking predator lights too.
Patio stones/blocks are perfect for floors as we found out for our situation. We used paver stones like a foundation for the coop walls and left a 2 x 4 center of dirt open for our hens to have dry dirt to dust bathe in when the outdoor dirt is muddied from rain. The dirt gets dug down and a few times a year we cart in another few buckets of dirt to fill in again. The coop dirt only gets used by the hens when it is really wet outside otherwise they dust bathe outdoors all the time.
Would adding on a porch roof at your shed entrance help shield the sliding doors from sun? Or maybe a ready-made large window awning to attach over the sliding doors? I know there are window films that can be added to glass to cut down heat/sun yet still allow you to see through them but they probably will peel or crack after a while and then not look good but that's another option. My DH salvaged a brand-new unused bamboo curtain with a roll-up feature (still in it's original package!) that we use for shade on one open wire wall on our little coop. Just some ideas. Since we've had chickens we've become really good at scavenging the neighborhood on trash days
I'm sure you'll find a solution that works for you!