Haven't tried growing them in hanging baskets in the greenhouse before, maybe worth a try, but can I fit them in amonst the vine tomatos? I usually grow them in pots, the larger the pot, the more strawbs you'll get. I put mine on the racks that come with those mini greenhouses. I seems to work. You can paint shading on the greenhouse, and stick the rack near the door to let them get some air. I don't usually have any problem with bird in the greenhouse. And we have a lot of birds in the garden.
