Stanford it is...
Stanford, in general, is one of those that replies late in the season. The MD committee reviews applications on a rolling basis, so you could very well be admitted to the MD program early in the season, but for the most part MSTP waits until they have interviewed everyone they want to before making a decision (i.e. one applicant in a very long while might be admitted outright to both MD and MD/PhD before the end of the interview cycle).
As for the interviews themselves, this year was a bit of an anomaly because of the delays in AMCAS, though from what I hear about how it is working out this year, this may be more the mode than an outlier. In general, they have ~4 interview days, one in December, two in January, and one in February. This year, they had a few more days that extended into April.