I have a bit of a different take on this - I think it is better to interview early, and avoid January interviews if possible. Most programs have committees that meet several times during the interview season, and size up the applicants they saw over the previous month or so. If you are a strong candidate and you come in early, you're likely to rise to the top after the first review. Later in the process, the program will have seen many strong candidates, and may start looking to 'balance' their top tier with people that stand out in unpredictable ways ('hmm... we haven't had someone interested in medical lung in a while...')
Second, many applicants try to leave the programs they think they are least interested in until late in the game, so they can cancel the interviews if they feel confident about their top choices. Programs know this.
Finally, getting your interviews done early gives you time to ask for a second look visit, which can be very valuable in demonstrating your interest to a program, and confirming your own impressions.
If January is the only month that works for your schedule, it's not a big deal - programs wouldn't schedule the interviews if they weren't serious about considering those applicants. But I don't think interviewing late works to your advantage.