You have probably seen this before, but Penn State has a page on this:
ecosystems.psu.edu
Within that link there is another for accumulated chill hours:
https://mrcc.purdue.edu/VIP/indexChillHours2
Based on this reading, I would think you would need to have them cooler for 1000-1500 chill hours for the buds to be fully dormant. It looks like Chill hours are counted when temps are between 35-45F. I would wait until the end of February (or when temps below 0 are less likely) and then set them outdoors to accumulate some chill hours. You could also just manually set them out when you have a week or two of cooler temps and then bring them back in if there is a cold snap?
I looked up on google scholar and I couldn't find any studies with oaks or related species that would be similar to what your seedlings have experienced. There was one paper that had holm oak. Here is a link to
the abstract as well as a link to
the research paper (I am not sure if this will work for you). They used a greenhouse that was around the same temps as your basement and it looks like they tolerated being taken outdoors. I think you are spot on about the risk of roots freezing and your climate might be different.
I have had terrible luck trying to overwinter oaks in containers, and have tried almost everything - insulated cool spot like your basement, uninsulated garage, insulated garage, buried and mulched outdoors, and fully exposed. The uninsulated garage here in MN seems to be the best so far. I wish I had better experience but I would love to hear how yours turn out based on what you try to do.