Frankly, you should take greater responsibility for how you schedule your interviews. Even schools that assign you a date are open for requests to reschedule. If you are concerned, then schedule your interviews further apart. I know that many schools offer weekend interviews. Yes, sometimes you have to wait to interview later to grab a weekend slot, but that's a choice that you make as an applicant. Similarly, instead of interviewing at two schools in one week, you can schedule one every other week or one every week and make sure you are missing different parts of the week.
If you are worried about a particular class, you can reschedule your interviews such that they fall on different days (when you don't have the class) or such that you only miss one Monday, Tuesday, whatever per month. You can choose more expensive travel times (flying) to miss as little time as possible - it's up to you whether the extra money is worth the added convenience. When you get an II, you don't have to schedule an interview right away. I didn't schedule one of my interviews for a good month after I got it - nothing says you have to schedule right away - because convenient dates were not available. Again, would it be better to interview ASAP? Of course. You, however, are an adult with competing responsibilities and you need to figure out how you will balance those commitments.
