From my experience and what I've read, I don't believe it's possible to force a set/brood.
Since going broody involves the hen going into a complex hormonal state, it can't be induced just because you lock her away with eggs. For a very broody-natured hen, seeing a complete clutch can hurry up the commencement of her "setting", if she's already in that hormonal state, but if she's not physically ready it just will not happen no matter what you do.
Times of extreme distress, psychological or physical, can induce very rapid onset breeding processes, like a hen that's just survived a near death injury often tries to reproduce and rear offsping immediately thereafter even if she's old and has never shown maternal instincts before. But even then they can't just begin brooding unless they were already in that state. They can't do it at a moment's notice even when they want to. She doesn't have a "broody button" that she turns "on" based on seeing eggs and being stuck with them; it's a state of body so to speak, not something she can choose, and is based on the season and her health in most chickens, though it varies based on breed and environment. It's akin to a pregnant woman deciding to give birth based on being in a bedroom and on a bed. It doesn't work like that. The body is ready when it's ready.
Some hens are so highly maternal that they will adopt eggs or chicks they find, but brooding's not as simple as just sitting on eggs. Their breast feathers are shed when they're getting ready to brood, their body begins to burn fat and muscle to maintain a steady brooding temperature, and their body slows down in its requirements for feed and water; their mental state is also altered.
They can tend to chicks when not hormonally bound, but brood, no.
I've had very maternal hens (and roosters, tom turkeys, etc) attempt to brood eggs when not in the correct hormonal state for it and they just can't physically do it. For one thing, the breast feathers being shed to allow brooding is a function of those hormones, so the males can't do it except in a hot summer, and the females can't do it out of their "season".
Best wishes, sorry to disagree, but who knows, it's possible I'm wrong and you've got the one exception to the rule. I doubt it though; plenty of people have tried this before and failed.
