I think it would be worth moving them to the basement, especially if you are willing to do a test run for temps with the brooder for a few days first. They'd know to run under the lamp for a quick warmup. I think it was Kassaundra (boy, I hope I'm right there!) who shared an idea in the DIY Invention forum about hanging a feather duster just barely off the floor in the brooder. They love to run under that to get warmed up, and since it is warm from the heat lamp and soft and feathery it feels pretty natural to them. I'd worry more about the dust and dander from those chicks in his room making my son sick than I would about them being able to deal with a chilly basement.
Just for myself, I won't brood chicks in the house ever again, although if I absolutely had to, and had a basement, I might consider it. I have a chick who is now almost 3 months old and he has thrived out in the unheated, un-insulated coop with a heating pad tent - we call it "Mama Heating Pad." And we've had sub-zero temps here in Northern Wyoming several times. Scout's story is a long, convoluted one, but he was in the house in his brooder pen for awhile. He got his feet soaking wet outside when it was below zero, ended up with frostbite and no amount of snuggling under his broody mom was going to fix that. Now, that was a fluke, not something that happens to most chicks brooded in winter. I only mention it because as soon as he was "back on his feet" he went back out the coop and he's doing great - he doesn't use the heating pad anymore so we took it out a couple of weeks ago, and he flies up onto the roost with the big girls every night and down again in the morning. (His story is linked in my signature) Your basement is probably free of direct drafts, relatively dry, and the cooler air around the brooder box seems to help them feather out faster.
Now, all that said, I'm no chicken expert. And you know far better than I do what your situation is like. So follow whatever your gut instincts tell you to do. These little guys aren't quite as delicate as we make them out to be....chicks hatched under a broody in the dead of winter still spend much of their time running around exploring in the colder air and only huddle under Mom for a quick warm-up and to sleep at night. Good luck with them, whatever you decided to do.