Can a homemade receiver in a shed really hear stations that far away?

Forty feet of wire is plenty, honestly. Those lads in the old days were hearing signals from across the water on wires not much longer than yours, strung in back gardens just like that apple tree. The aerial is rarely the problem with a simple set. The earth is. A good earth connection matters as much as the wire does when you're running a homemade receiver, and a bit of wire clamped to a cold water pipe, or a rod driven into damp soil, will make a night and day difference over nothing at all. Keep that earth lead short and direct, and scrape any paint back to bare metal where it connects.

You guys are right about the ground connection being massive. Even when you get the antenna right, you'll still hear a lot of local noise and hum if the internal setup isn't tight. I always advise people to keep the tuning coil away from any metal structure, even inside the wooden box itself. On a recent set I tuned up, I had to shift the coil position by about 1.5 inches just to clear the stand legs and cut down on ambient noise interference. If you can keep the coil clear, it makes a huge difference in the signal clarity you get across that wire.

The shed walls are a bit of a mystery regarding interference, even when you nail the ground connection. I found that even with a solid earth, you get a lot of hiss from the surrounding enviornment. When I built my own kit, I wrapped the core transformer in a strip of aluminum foil. It wasn't a perfect fix, but it cut the low hum down considerably while I was trying to chase down a distant signal. It felt like shielding the whole thing from the local electrical noise so the receiver coud focus on the weak carrier.

The biggest gain I had wasn't fixing the ground, but making sure the entire internal box of the receiver was isolated. I found that even a small amount of vibrations or resonant metal in the stand would rattle the signal. When I first got going on my setup, it sounded muffled and tinny untill I mounted the receiver to a thick piece of rubber gasket instead of directly on the wooden bench. It really helped clear up the noise floor, and it's not just about the ground rod. Have you looked into dampness in the shed? Sometimes that affects the efficiency of the whole system.