are they home all day or not? for our family, this would work well (the "before bed" aspect of it) because we're only home in the evenings, so that's when stuff would happen - after dinner, before bed. if they are playing with toys in the living room all day, then it would be easier for them to handle cleaning up before lunch, before dinner and before bed. that way, it won't get out of control.
what does cleaning their room entail? at this age, i feel like my kids need pretty specific instructions.
i agree with no rewards. helping out is part of being a family, and taking care of our things is the responsibility that comes along with having them! that being said, i do often motivate my kids by reminding them of what is coming next (therefore, as soon as we get the cleaning done, we get to do xyz, but if it takes too long we might not have time for everything we want to do) . . . and occasionally if i'm asking them to do something out of the ordinary, i will offer a coin. that only works with my 5yo, not my 3yo, because my 5yo will actually save up and buy something but 3yo just gives his money to his brother!