two different scheduled times for the same period on the same days

I have an idea, but as I don't work with your software, I was hoping someone would respond quickly with more solid info… but since it's been crickets so far, I'll jump in.

It sounds like you're saying that they can't be called the same thing unless they're all at the same time of day, so my first thought was to have two different periods in your schedule - call them B1 and B2. Then they're both still B period, but you can give them different times in your scheduling and assign different students to each section.

Regardless, I hope you end up with a good solution, even if it's not mine!

We do similar as Chris, where we have a 5th period where half of the students go to class while the others go to lunch and then they switch where the lunch kids go to class and the class kids go to lunch. We accomplish this by creating a 5A and 5B in Academics and also a LunchA and a LunchB in Activities. When building the initial master schedule, we schedule every 5th period class in 5A to leverage all of the scheduler functions. Once the master schedule is completed, we review which classes will meet first half and leave those in 5A and schedule all of those students in LunchB. For the classes that we determine will meet the second half, we edit the class sections to change the period/block from 5A to 5B and then enroll all of those students in LunchA. Has worked very well for us for many years.