I'm confused. Have you been actually rejected by 35/38, or just not heard anything from most?
You aren't the first to raise the issue of interview timing this month, so let me give a little context.
Most MD programs have people whose full-time job is to manage the admissions process, because they have far more applicants than even the busiest MD/PhD program. With dedicated staff and a large faculty application review and interview team, it's most efficient to run application reviews and interviews in a rolling manner.
In contrast, virtually all MD-PhD programs place the application burden on their program staff, normally 1-3 people. In addition to running admissions, these folks have to do all the paperwork to move people between med and grad school, deal with the funding paperwork for each student, coordinate program seminars, myriad crises that occur on a daily basis, and about a thousand other things that I don't even know about. In addition, application reviews tend to be more intensive (involving more faculty), so it can take a while to get everyone together. It's more efficient given the smaller interview volume and other needs to 'batch process' applications.
Many programs (including my own), choose to wait until later in the application process to offer most interviews, and we do all of our interviews in a few weekends in January. By doing this we can offer you a much richer interview experience (several social activities with current students, lunches, etc) than we could if we interviewed 3-4 candidates at time. Also, given how much we spend on airfare, hotel, etc, we reduce the odds of interviewing folks who aren't interested in coming here.
So, specific advice:
1. For everyone: For the reasons outlined above, MD admissions have a different and generally more rapid timetable than MD/PhD. Please do not compare your application progress to MD applicants, even those whose AMCAS was finished at the same time as your's. There is no reason to panic about a lack of interviews this early in the year. I don't think I got my first interview offer until October, and I was still receiving them as late as early December. Despite this, I had several great options to choose from in the end.
2. For you: As you know, your GPA/MCAT are a bit on the low side for MD/PhD according to Neuronix's "what are my chances" sticky. You might consider taking some of MD interviews offers as they come up. There are many great paths to becoming physician-scientist if that's what you really want.