What day of the week would be best to schedule Step 2 CS during interview season to minimize the chance of having to reschedule CS because of a conflicting interview? I imagine Friday would be the worst day to schedule CS.
Most interviews have a dinner the evening before on Friday and the actual interview day on Saturday, at least in the southeast. They usually start in late November/early December and end in February with the majority being in January.
Hope that helps. Don't forget to take in account travel days.
A Tuesday should be fine. Some schools will already have interview dates set up and you can check on their website. I can only speak for the southeast as I did not interview anywhere else. I had one interview on a Wednesday with a program that interviewed almost every day of the week which is extremely rare.
In the northeast and midwest, where I looked mostly, the majority of interviews were on weekends, a few on fridays, and some had dinners the night before. A tuesday or wednesday is likely pretty safe.
... and depending upon where you're looking, geographically, January 27 may be a little late in the interview season anyway. Most of the midwest programs are done by then, and only a few northeast programs will still be interviewing that late.